EDP Sciences
1711650699
20240328
fre
laboutique.edpsciences.fr-002230
03
01
002230
03
9782759827879
15
9782759827879
00
BA
02
16
mm
01
24
mm
10
01
02
Enseignement SUP-Maths
01
01
Mathématiques supérieures
Cours - Tome 1
1
A01
01
A2119
Alexander Gewirtz
Gewirtz, Alexander
Alexander
Gewirtz
<p>Alexander Gewirtz est professeur agrégé, docteur en mathématiques. Il est responsable du département mathématiques, enseignant à l'IFCEN (Institut franco-chinois de l'énergie nucléaire) à Zhuhai en Chine. </p>
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fre
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454
03
01
24
Izibook:Subject
Mathématiques
20
séries numériques;algèbre;espaces vectoriels normés;suite de fonctions;séries de fonctions;introduction au calcul différentiel
10
MAT030000
29
CLIL3052
01
510
05
03
00
<p><blockquote> L’objectif de ce premier tome est d’introduire tous les fondements d’algèbre (les structures), d’algèbre linéaire (les espaces vectoriels et applications linéaires) et d’analyse (les concepts de limite en particulier pour les suites ou les fonctions). La volonté de ne pas séparer algèbre et analyse en deux tomes différents s’inscrit dans une démarche pédagogique visant à briser l’idée que ces domaines sont disjoints et comprendre que des techniques « algébriques » peuvent s’appliquer pour des questions d’analyse et réciproquement. Ce livre a été rédigé comme support de cours pour les étudiants de l’IFCEN mais aussi comme outil de travail pour des élèves de classes préparatoires ou de premier cycle universitaire. Il pourra d’ailleurs également intéresser les candidats aux concours de recrutement des enseignants. Ainsi, les prérequis pour chaque chapitre sont explicitement donnés, les preuves des propriétés sont complètes et très détaillées, de nombreux exemples et exercices d’applications directes sont donnés et enfin, de nombreux points méthodes sont indiqués. En complément, une large sélection d’exercices (de difficulté variable) est proposée à la fin de chaque chapitre, permettant ainsi de « pratiquer » ce qui a été appris et proposant parfois une ouverture sur des sujets plus avancés. Enfin, certains chapitres proposent également une annexe avec des compléments pour les étudiants désireux d’approfondir leurs connaissances en mathématiques.</blockquote>Ce livre est inspiré des cours de mathématiques proposés à l’institut franco-chinois de l’énergie nucléaire (IFCEN), situé à Zhuhai dans la province du Guangdong en Chine.</p>
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<p>Cours de mathématiques pour les deux premières années de licence scientifique et classes préparatoires</p>
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<p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 1 Groupes, anneaux et corps 7<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1 Groupes . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.1 Loi decomposition interne . . . . . . . . . . . . . . . . . . . . . . . 8<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.2 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition d<span lang="EN-US">’</span>un groupe et r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gles de calcul . . . . . . . . . . . . . . . 13<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.3 Sous-groupes . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.4 Op</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rations sur les sous-groupes . . . . . . . . . . .. . . . . . . . . 20<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.5 Morphismes degroupes . . . . . . . . . . . . . . . . . . . . . . . . . 22<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2 Anneaux et corps .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finitions . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 28<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.2 Sous-anneaux etsous-corps . . . . . . . . . . . . . . . . . . . . . . 29<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.3 R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gles de calcul dans un anneau . . . . . . . . . . .. . . . . . . . . 32<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.4 Op</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rations sur les sous-anneaux et sous-corps . . . .. . . . . . . . 36<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.5 Morphismes d<span lang="EN-US">’</span>anneaux (ou de corps) . . . . . . . . . . . . . . . . . 37<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.3 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 2 Relations, ensembles </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">N</span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">, </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">, </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Q </span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">et </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R </span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">47<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1 Relations . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.1 G</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ralit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s sur lesrelations . . . . . . . . . . . . . . . . . . . . . . 48<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2 Relation d<span lang="EN-US">’</span>ordre . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 50<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2.a Ordre total etordre partiel . . . . . . . . . . . . . . . . . 52<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2.b Majorant,minorant, plus grand et plus petit </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">l</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ment . . . 53<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2.c Borne sup</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieure et borne inf</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieure. . . . . . . . . . . . 56<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2.d Applicationscroissantes, d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ecroissantes et monotones . . . 58<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.3 Relation d<span lang="EN-US">’</span></span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quivalences . . . . . . . . . . . . . . . .. . . . . . . . . 60<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">N </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et principe de r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence . . . .. . . . . . . . . . . . . . . . . 61<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition de l<span lang="EN-US">’</span>ensemble</span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">N </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . .. 61<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2 Principe de r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence . . . . . . . . . . . . . . . . . . . . .. . . . 62<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2.a R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence simple . . . . . . . . . . . . . . . . . .. . . . 62<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2.b R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence double . . . . . . . . . . . . . . . . . .. . . . 65<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2.c R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence forte . . . . . . . . . . . . . . . . . .. . . . . 66<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2.d r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence finie et r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currencedescendante . . . . . . . . . 67<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.3 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et valeur absolue . . . . . . . . . . . . . . . . .. . . . . . . . 69<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.3.1 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et structure d<span lang="EN-US">’</span>anneau . . .. . . . . . . . . . . . . . . . 69<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.3.2 Valeur absoluedans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . .. . . 71<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4 Ensembles desnombres r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">els . . . . . . . . . . . . . . . . . . . . . . . .. . 71<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.1 Corps desnombres rationnels . . . . . . . . . . . . . . . . . . . . . 71<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.2 Corps desnombres r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">els et relation d<span lang="EN-US">’</span>ordre . .. . . . . . . . . . . . 72<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.3 Valeur absolue .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.4 Propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s de la borne sup</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieure et de la borne inf</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieure . . . . . 75<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.5 Partie enti</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">re . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 79<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.6 Caract</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">risation des intervalles de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . 81<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.7 Droite num</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rique achev</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">e . . . . . . .. . . . . . . . . . . . . . . . 84<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.8 Densit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Q </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">etde </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">\ </span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Q </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . . . . 84<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.9 Valeurs d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">cimales approch</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">es d<span lang="EN-US">’</span>un nombre r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">el . . . . . . . . . . . 87<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.5 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6 Annexe . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.1 Construction de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . . . . . .. 96<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2 Ensembles finiset d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">encombrements . . . . . . . . . . . . . . . . . . .105<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.a D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finitions et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me fondamental . . . . . . . . . . . . 105<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.b Parties de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">N </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et parties d<span lang="EN-US">’</span>un ensemblefini . . . . . . . . . 109<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.c Crit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">re de bijection pour les ensembles finis . . . . .. . . 114<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.d D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">nombrement . . . . . . . . . . . . . . . . . . . .. . . . 117<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.e Cardinal d<span lang="EN-US">’</span>une r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">union et du compl</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mentaire d<span lang="EN-US">’</span>une partie 117<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.f Produit cart</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">sien . . . . . . . . . . . . . . . . . . . . . . .117<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.g Ensemble desapplications de </span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">E </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">vers </span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">F </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . 118<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.h Cardinal de </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">P</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">E</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">) .. . . . . . . . . . . . . . . . . . . . . 119<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.i Arrangements,nombres d<span lang="EN-US">’</span>injections et nombres de bijections<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">d<span lang="EN-US">’</span>unensemble dans lui-m</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ê</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . 121<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.j Combinaisonset coefficients binomiaux . . . . . . . . . . . 123<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.k Propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s des coefficients binomiaux . . . . . . . .. . . . 124<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 3 Suites de nombres réels ou complexes125<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.1 Suites de nombres r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">els . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 126<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.1.1 G</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ralit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 126<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.1.2 Operations surles suites . . . . . . . . . . . . . . . . . . . . . . . . 129<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.1.3 Suites extraites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.2 Suites d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finies par une relation de r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence . . . . . . . . . . . . . . . . . 135<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.2.1 Suites arithm</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">tiques et g</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">om</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">triques . . . . . . . . . . . . . . . . . 136<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.2.2 Notations <span lang="EN-US">Σ</span> et <span lang="EN-US">Π</span> . . . . . . . . . . . . . . .. . . . . . . . . . . . . 137<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.2.3 Suites r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currentes lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires d<span lang="EN-US">’</span>ordre 2 `a coefficients constants . . . . 142<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3 Limite d<span lang="EN-US">’</span>une suite . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 150<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.1 Convergence versun r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">el</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12"> </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">: d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition et propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s . . . . . . . . . 150<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.2 Convergence etsigne . . . . . . . . . . . . . . . . . . . . . . . . . . 154<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.3 Divergence d<span lang="EN-US">’</span>une suite . . . . . . . . . . . . . . . . . . . . . . . . .155<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.3.a Divergencevers +</span><i><span lang="EN-US" style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">∞ </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ou vers </span><i><span lang="EN-US" style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">−∞ </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. .. . . . . . . . . . . . 156<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.3.b Autres modesde divergence . . . . . . . . . . . . . . . . . 157<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.4 Operations surles suites convergentes . . . . . . . . . . . . . . . . . 158<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3 Math</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">matiques sup</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieures 1 <o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.4.a Espacevectoriel des suites convergeant vers 0 . . . . . . . 158<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.4.b Operations alg</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">briques sur les limites . . . . . . . . . . . . 160<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.5 Compatibilit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> du passage </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> la limite avecla relation d<span lang="EN-US">’</span>ordre . . . . 164<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.6 Convergence etsuites extraites . . . . . . . . . . . . . . . . . . . . 169<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.7 Caract</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">risation de la densit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> parles suites . . . . . . . . . . . . . . 173<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes d<span lang="EN-US">’</span>existence delimite . . . . . . . . . . . . . . . . . . . . . . . . 174<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4.1 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes de convergence et de divergence monotone. . . . . . . . 174<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4.2 Application du th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de la limite monotone aux s</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ries </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> termes<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">positifs . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 178<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4.3 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me des suites adjacentes et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me des segments emboit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s 187<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4.4 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de Bolzano-Weierstrass . . . . . . . . .. . . . . . . . . . 190<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5 Relations de comparaison. . . . . . . . . . . . . . . . . . . . . . . . . . . 192<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5.1 Suites domin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">es ou n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gligeables parrapport </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> une autre . . . . . . 192<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5.2 Suites </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quivalentes . . . . . . . . . . . . . . . . . . . .. . . . . . . 193<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5.3 Comparaison dessuites de r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">f</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rence . . . . . . . . . . . . . . . . . .198<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5.4 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">veloppement asymptotique d<span lang="EN-US">’</span>unesuite . . . . . . . . . . . . . . . 199<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.6 Suites `a valeurscomplexes . . . . . . . . . . . . . . . . . . . . . . . . . . . 202<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.6.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finitions et convergence d<span lang="EN-US">’</span>unesuite complexe . . . . . . . . . . . 202<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.6.2 Lien avec lesparties r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">elle et imaginaire . . . . . . . . . . . . . . .204<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.7 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 4 Espaces vectoriels et applications linéaires215<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.1 Espaces vectoriels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.1.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition et exemples usuels . . . . . . . . . . . .. . . . . . . . . . 216<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.1.2 R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gles de calcul dans un espace vectoriel . . . . . .. . . . . . . . . 219<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.1.3 Sous-espacesvectoriels . . . . . . . . . . . . . . . . . . . . . . . . . 221<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2 Operations sur lesespaces vectoriels . . . . . . . . . . . . . . . . . . . . . . 225<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2.1 Intersection etsous-espace engendre par une partie . . . . . . . . . 225<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2.2 Somme desous-espaces vectoriels . . . . . . . . . . . . . . . . . . . 232<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2.3 Sommes directeset sous-espaces vectoriels suppl</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mentaires . . . . . 236<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2.4 Produit cart</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">sien de deux espaces vectoriels . . . . . . . . . .. . . 241<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3 Sous-espacesaffines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3.1 Translations etgroupes des translations d<span lang="EN-US">’</span>un espace vectoriel . . . .243<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3.2 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition d<span lang="EN-US">’</span>un sous-espaceaffine . . . . . . . . . . . . . . . . . . . 244<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3.3 Parall</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">lisme . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 247<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3.4 Intersection dedeux sous-espaces affines . . . . . . . . . . . . . . . 248<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4 Applications lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 249<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition et exemples . . . . . . . . . . . . . . .. . . . . . . . . . 249<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.2 Noyau et image d<span lang="EN-US">’</span>une application lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aire . . . . . .. . . . . . . . . 253<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.3 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">Equations lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires . . . . .. . . . . . . . . . . . . . . . . . . . . . 258<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.4 Ensembles desapplications lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">L</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">E,F</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">) . . . . . . . . . . . . . 259<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.5 Isomorphismes,automorphismes et groupe lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires . . . . . . . . . . 263<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.6 Restriction etrecollement . . . . . . . . . . . . . . . . . . . . . . . 265<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.7 Hyperplans d<span lang="EN-US">’</span>un espace vectoriel et formes lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires . . . . . . . . . 268<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.8 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">Etude d<span lang="EN-US">’</span>applications lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires remarquables . . . . . . . . . . . . . 271<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.8.a Homoth</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ties . . . . . . . . . . . . . . . . . . . . . . .. . 271<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.8.b Projecteurs .. . . . . . . . . . . . . . . . . . . . . . . . . 272<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.8.c Sym</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">tries . . . . . . . . . . . . . . . . . . . . . . .. . . . 276<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.5 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 5 Arithmétique dans </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">287<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1 Arithm</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">tique dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 288<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.1 Diviseurs etcongruences . . . . . . . . . . . . . . . . . . . . . . . . 288<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.2 Nombres premierset d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">composition en produit de facteurs premiers 291<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.3 Divisioneuclidienne . . . . . . . . . . . . . . . . . . . . . . . . . . . 294<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.4 Sous-groupes de(</span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">,</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">+) .. . . . . . . . . . . . . . . . . . . . . . . . 295<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.5 Plus grandcommun diviseur et plus petit commun multiple . . . . 296<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.6 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de B</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">zout etalgorithme d<span lang="EN-US">’</span>Euclide . . . . . . . . . . . . . 298<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.7 Lemme d<span lang="EN-US">’</span>Euclide et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de Gauss . .. . . . . . . . . . . . . . 302<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.2 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.3 Annexe . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.3.1 Anneaux </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">/n</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et quelques propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s . . . . . . . . . . . . . . . . . 310<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.3.2 Corps </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">/p</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">l</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mentsinversibles de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">/n</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . 312<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 6 Fonctions r´eelles ou complexes d’unevariable réelle 313<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1 G</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ralit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s sur lesfonctions d<span lang="EN-US">’</span>une variable r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">elle . . . . . . . . . . . . . . . 314<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.1 Ensemble </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">F</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">I,</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">)et relation d<span lang="EN-US">’</span>ordre . . . . . . . . . . . . . . . . .314<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.2 Ensemble </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">B</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">I,</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">). . . . . . . . . . . . . . . . . . . . . . . . . . . . 315<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.3 Fonctions p</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">riodiques . . . . . . . . . . . . . . . . . . . . .. . . . . 317<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.4 Fonctions paireset fonctions impaires . . . . . . . . . . . . . . . . . 318<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.5 Fonctionslipschitziennes . . . . . . . . . . . . . . . . . . . . . . . . 320<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.6 Fonctionsmonotones . . . . . . . . . . . . . . . . . . . . . . . . . . 322<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">Etude locale d<span lang="EN-US">’</span>une fonction. . . . . . . . . . . . . . . . . . . . . . . . . . 323<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.1 Voisinage d<span lang="EN-US">’</span>un point . . . . . . . . . . . . . . . . . . . . . . . . . .323<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.2 Limite d<span lang="EN-US">’</span>une fonction en un point et continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> en un point . . . . . 325<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.3 Operations alg</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">briques sur les limites . . . . . . . . . . . . . .. . . 335<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.4 Compatibilit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> du passage </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> la limite avecla relation d<span lang="EN-US">’</span>ordre dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">341<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.5 Composition delimites et caract</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">risation s</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quentiellede la limite . 348<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.6 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de la limite monotone . . . . . . . . . .. . . . . . . . . . 353<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3 Relations decomparaisons . . . . . . . . . . . . . . . . . . . . . . . . . . . 356<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3.1 Fonctions domin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">es et fonctions n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gligeablespar rapport `a une autre<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">au voisinage d<span lang="EN-US">’</span>un point . . . . . . . . . . . . . . . . . . . . . . . . .356<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3.2 Comparaison desfonctions usuelles . . . . . . . . . . . . . . . . . . 363<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3.3 Fonctions </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quivalentes en un point . . . . . . . . . . . . . .. . . . 364<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3.4 Equivalentsusuels . . . . . . . . . . . . . . . . . . . . . . . . . . . 368<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4 Continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> globale . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 372<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition et premi7res propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s . . . . . . . . . . . . . . . . . . . 372<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.2 Compos</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">e de deux fonctions continues . . . . . . . . . . .. . . . . 374<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.3 Restriction et caract</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">re </span><span style="font-size:9.5pt;font-family:LMRoman12-Regular;mso-bidi-font-family:LMRoman12-Regular">« </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">local </span><span style="font-size:9.5pt;font-family:LMRoman12-Regular;mso-bidi-font-family:LMRoman12-Regular">» </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">de la continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> . . . . . . . .. . . 375<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.4 Prolongement parcontinuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> . . . . . . . . . . . . . . . . . . . . . . 376<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.5 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me des valeurs interm</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">diaires . . . . . . . . . . . . . . . . . 378<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.6 Image d<span lang="EN-US">’</span>un segment par une fonction continue . . . . . . . . . . . .381<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.7 Continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> de la bijection r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ciproque. . . . . . . . . . . . . . . . . 383<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.8 Continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> uniforme et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de Heine . . . . . . . . . . . . . . 384<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.5 Bilan sur les diff</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rences entre fonctions `a valeurs r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">elles ou complexes . . . 389<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.6 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 7 Polynômes et fractions rationnelles 396<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 397<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1.1 Alg</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">bres et morphisme d<span lang="EN-US">’</span>alg</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">bres . . . . . . . . . . . . . . . . . . . 397<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1.2 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition d<span lang="EN-US">’</span>un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . . . . . . . . . . .401<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1.3 Operationsusuelles sur les polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes . . . . . . . . . . . . . . . . . 401<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1.4 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rivation sur l<span lang="EN-US">’</span>ensemble despolyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes . . . . . . . . . . . . . . . 409<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.2 Degr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> d<span lang="EN-US">’</span>un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 412<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.2.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 412<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.2.2 Propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s du degr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> . . . . . . . .. . . . . . . . . . . . . . . . . . . 413<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.2.3 Cons</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quences fondamentales . . . . . . . . . . . . . . .. . . . . . . 414<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3 Arithm</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">tique dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] .. . . . . . . . . . . . . . . . . . . . . . . . . . . 415<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.1 Divisibilit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] .. . . . . . . . . . . . . . . . . . . . . . . . 415<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.2 Divisioneuclidienne dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] .. . . . . . . . . . . . . . . . . . . 419<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.3 Id</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aux de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 423<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.4 Polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes premiers entre eux . . . . . . . . . . . . . .. . . . . . . 425<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.5 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de B</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">zout et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de Gauss . . . . . . . . . . . . . . 427<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4 Racines d<span lang="EN-US">’</span>un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 429<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.1 Fonctionpolynomiale associ</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">e </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . 429<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.2 Racines d<span lang="EN-US">’</span>un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . . . . . . . . .. . . . 430<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.3 Formule deTaylor et multiplicit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> d<span lang="EN-US">’</span>une racine . . .. . . . . . . . . 432<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.4 M</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">thodes pour montrer que deux polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes sont </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gaux . . . . . .436<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.5 Polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes scindes et relations entre racines etcoefficients . . . . . 437<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.5 Polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes irr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ductibles etfactorisation . . . . . . . . . . . . . . . . . . . . 439<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.5.1 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">El</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ments irr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ductibles dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">C</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] . . . . . . . . . . . . . . . . . . . 440<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.5.2 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">El</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ments irr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ductibles dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] . . . . . . . . . . . . . . . . . . . 441<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">) . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 442<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6.1 Corps desfractions rationnelles </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">) .. . . . . . . . . . . . . . . . 442<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6.2 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rivation et degr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> . . . . . . . .. . . . . . . . . . . . . . . . . . . 443<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6.3 Z</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ros et p</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">les d<span lang="EN-US">’</span>une fraction rationnelle . . . . . . . . . . . . . . . . 445<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6.4 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">composition en </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">l</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ments simples . . . . . . . . . . . . . . . . . .446<o:p></o:p></span></p><p></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.7 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448<o:p></o:p></span></p>
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Alexander Gewirtz
Gewirtz, Alexander
Alexander
Gewirtz
<p>Alexander Gewirtz est professeur agrégé, docteur en mathématiques. Il est responsable du département mathématiques, enseignant à l'IFCEN (Institut franco-chinois de l'énergie nucléaire) à Zhuhai en Chine. </p>
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séries numériques;algèbre;espaces vectoriels normés;suite de fonctions;séries de fonctions;introduction au calcul différentiel
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<p><blockquote> L’objectif de ce premier tome est d’introduire tous les fondements d’algèbre (les structures), d’algèbre linéaire (les espaces vectoriels et applications linéaires) et d’analyse (les concepts de limite en particulier pour les suites ou les fonctions). La volonté de ne pas séparer algèbre et analyse en deux tomes différents s’inscrit dans une démarche pédagogique visant à briser l’idée que ces domaines sont disjoints et comprendre que des techniques « algébriques » peuvent s’appliquer pour des questions d’analyse et réciproquement. Ce livre a été rédigé comme support de cours pour les étudiants de l’IFCEN mais aussi comme outil de travail pour des élèves de classes préparatoires ou de premier cycle universitaire. Il pourra d’ailleurs également intéresser les candidats aux concours de recrutement des enseignants. Ainsi, les prérequis pour chaque chapitre sont explicitement donnés, les preuves des propriétés sont complètes et très détaillées, de nombreux exemples et exercices d’applications directes sont donnés et enfin, de nombreux points méthodes sont indiqués. En complément, une large sélection d’exercices (de difficulté variable) est proposée à la fin de chaque chapitre, permettant ainsi de « pratiquer » ce qui a été appris et proposant parfois une ouverture sur des sujets plus avancés. Enfin, certains chapitres proposent également une annexe avec des compléments pour les étudiants désireux d’approfondir leurs connaissances en mathématiques.</blockquote>Ce livre est inspiré des cours de mathématiques proposés à l’institut franco-chinois de l’énergie nucléaire (IFCEN), situé à Zhuhai dans la province du Guangdong en Chine.</p>
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<p>Cours de mathématiques pour les deux premières années de licence scientifique et classes préparatoires</p>
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<p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 1 Groupes, anneaux et corps 7<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1 Groupes . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.1 Loi decomposition interne . . . . . . . . . . . . . . . . . . . . . . . 8<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.2 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition d<span lang="EN-US">’</span>un groupe et r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gles de calcul . . . . . . . . . . . . . . . 13<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.3 Sous-groupes . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.4 Op</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rations sur les sous-groupes . . . . . . . . . . .. . . . . . . . . 20<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.1.5 Morphismes degroupes . . . . . . . . . . . . . . . . . . . . . . . . . 22<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2 Anneaux et corps .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finitions . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 28<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.2 Sous-anneaux etsous-corps . . . . . . . . . . . . . . . . . . . . . . 29<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.3 R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gles de calcul dans un anneau . . . . . . . . . . .. . . . . . . . . 32<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.4 Op</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rations sur les sous-anneaux et sous-corps . . . .. . . . . . . . 36<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.2.5 Morphismes d<span lang="EN-US">’</span>anneaux (ou de corps) . . . . . . . . . . . . . . . . . 37<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">1.3 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 2 Relations, ensembles </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">N</span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">, </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">, </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Q </span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">et </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R </span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">47<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1 Relations . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.1 G</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ralit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s sur lesrelations . . . . . . . . . . . . . . . . . . . . . . 48<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2 Relation d<span lang="EN-US">’</span>ordre . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 50<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2.a Ordre total etordre partiel . . . . . . . . . . . . . . . . . 52<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2.b Majorant,minorant, plus grand et plus petit </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">l</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ment . . . 53<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2.c Borne sup</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieure et borne inf</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieure. . . . . . . . . . . . 56<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.2.d Applicationscroissantes, d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ecroissantes et monotones . . . 58<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.1.3 Relation d<span lang="EN-US">’</span></span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quivalences . . . . . . . . . . . . . . . .. . . . . . . . . 60<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">N </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et principe de r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence . . . .. . . . . . . . . . . . . . . . . 61<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition de l<span lang="EN-US">’</span>ensemble</span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">N </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . .. 61<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2 Principe de r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence . . . . . . . . . . . . . . . . . . . . .. . . . 62<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2.a R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence simple . . . . . . . . . . . . . . . . . .. . . . 62<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2.b R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence double . . . . . . . . . . . . . . . . . .. . . . 65<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2.c R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence forte . . . . . . . . . . . . . . . . . .. . . . . 66<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.2.2.d r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence finie et r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currencedescendante . . . . . . . . . 67<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.3 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et valeur absolue . . . . . . . . . . . . . . . . .. . . . . . . . 69<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.3.1 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et structure d<span lang="EN-US">’</span>anneau . . .. . . . . . . . . . . . . . . . 69<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.3.2 Valeur absoluedans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . .. . . 71<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4 Ensembles desnombres r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">els . . . . . . . . . . . . . . . . . . . . . . . .. . 71<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.1 Corps desnombres rationnels . . . . . . . . . . . . . . . . . . . . . 71<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.2 Corps desnombres r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">els et relation d<span lang="EN-US">’</span>ordre . .. . . . . . . . . . . . 72<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.3 Valeur absolue .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.4 Propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s de la borne sup</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieure et de la borne inf</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieure . . . . . 75<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.5 Partie enti</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">re . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 79<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.6 Caract</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">risation des intervalles de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . 81<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.7 Droite num</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rique achev</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">e . . . . . . .. . . . . . . . . . . . . . . . 84<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.8 Densit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Q </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">etde </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">\ </span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Q </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . . . . 84<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.4.9 Valeurs d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">cimales approch</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">es d<span lang="EN-US">’</span>un nombre r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">el . . . . . . . . . . . 87<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.5 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6 Annexe . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.1 Construction de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . . . . . .. 96<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2 Ensembles finiset d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">encombrements . . . . . . . . . . . . . . . . . . .105<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.a D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finitions et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me fondamental . . . . . . . . . . . . 105<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.b Parties de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">N </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et parties d<span lang="EN-US">’</span>un ensemblefini . . . . . . . . . 109<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.c Crit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">re de bijection pour les ensembles finis . . . . .. . . 114<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.d D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">nombrement . . . . . . . . . . . . . . . . . . . .. . . . 117<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.e Cardinal d<span lang="EN-US">’</span>une r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">union et du compl</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mentaire d<span lang="EN-US">’</span>une partie 117<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.f Produit cart</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">sien . . . . . . . . . . . . . . . . . . . . . . .117<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.g Ensemble desapplications de </span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">E </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">vers </span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">F </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . 118<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.h Cardinal de </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">P</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">E</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">) .. . . . . . . . . . . . . . . . . . . . . 119<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.i Arrangements,nombres d<span lang="EN-US">’</span>injections et nombres de bijections<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">d<span lang="EN-US">’</span>unensemble dans lui-m</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ê</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . 121<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.j Combinaisonset coefficients binomiaux . . . . . . . . . . . 123<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">2.6.2.k Propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s des coefficients binomiaux . . . . . . . .. . . . 124<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 3 Suites de nombres réels ou complexes125<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.1 Suites de nombres r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">els . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 126<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.1.1 G</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ralit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 126<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.1.2 Operations surles suites . . . . . . . . . . . . . . . . . . . . . . . . 129<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.1.3 Suites extraites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.2 Suites d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finies par une relation de r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currence . . . . . . . . . . . . . . . . . 135<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.2.1 Suites arithm</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">tiques et g</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">om</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">triques . . . . . . . . . . . . . . . . . 136<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.2.2 Notations <span lang="EN-US">Σ</span> et <span lang="EN-US">Π</span> . . . . . . . . . . . . . . .. . . . . . . . . . . . . 137<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.2.3 Suites r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">currentes lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires d<span lang="EN-US">’</span>ordre 2 `a coefficients constants . . . . 142<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3 Limite d<span lang="EN-US">’</span>une suite . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 150<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.1 Convergence versun r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">el</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12"> </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">: d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition et propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s . . . . . . . . . 150<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.2 Convergence etsigne . . . . . . . . . . . . . . . . . . . . . . . . . . 154<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.3 Divergence d<span lang="EN-US">’</span>une suite . . . . . . . . . . . . . . . . . . . . . . . . .155<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.3.a Divergencevers +</span><i><span lang="EN-US" style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">∞ </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ou vers </span><i><span lang="EN-US" style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">−∞ </span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. .. . . . . . . . . . . . 156<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.3.b Autres modesde divergence . . . . . . . . . . . . . . . . . 157<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.4 Operations surles suites convergentes . . . . . . . . . . . . . . . . . 158<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3 Math</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">matiques sup</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rieures 1 <o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.4.a Espacevectoriel des suites convergeant vers 0 . . . . . . . 158<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.4.b Operations alg</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">briques sur les limites . . . . . . . . . . . . 160<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.5 Compatibilit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> du passage </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> la limite avecla relation d<span lang="EN-US">’</span>ordre . . . . 164<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.6 Convergence etsuites extraites . . . . . . . . . . . . . . . . . . . . 169<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.3.7 Caract</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">risation de la densit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> parles suites . . . . . . . . . . . . . . 173<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes d<span lang="EN-US">’</span>existence delimite . . . . . . . . . . . . . . . . . . . . . . . . 174<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4.1 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes de convergence et de divergence monotone. . . . . . . . 174<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4.2 Application du th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de la limite monotone aux s</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ries </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> termes<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">positifs . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 178<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4.3 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me des suites adjacentes et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me des segments emboit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s 187<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.4.4 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de Bolzano-Weierstrass . . . . . . . . .. . . . . . . . . . 190<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5 Relations de comparaison. . . . . . . . . . . . . . . . . . . . . . . . . . . 192<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5.1 Suites domin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">es ou n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gligeables parrapport </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> une autre . . . . . . 192<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5.2 Suites </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quivalentes . . . . . . . . . . . . . . . . . . . .. . . . . . . 193<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5.3 Comparaison dessuites de r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">f</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rence . . . . . . . . . . . . . . . . . .198<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.5.4 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">veloppement asymptotique d<span lang="EN-US">’</span>unesuite . . . . . . . . . . . . . . . 199<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.6 Suites `a valeurscomplexes . . . . . . . . . . . . . . . . . . . . . . . . . . . 202<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.6.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finitions et convergence d<span lang="EN-US">’</span>unesuite complexe . . . . . . . . . . . 202<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.6.2 Lien avec lesparties r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">elle et imaginaire . . . . . . . . . . . . . . .204<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">3.7 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 4 Espaces vectoriels et applications linéaires215<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.1 Espaces vectoriels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.1.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition et exemples usuels . . . . . . . . . . . .. . . . . . . . . . 216<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.1.2 R</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gles de calcul dans un espace vectoriel . . . . . .. . . . . . . . . 219<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.1.3 Sous-espacesvectoriels . . . . . . . . . . . . . . . . . . . . . . . . . 221<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2 Operations sur lesespaces vectoriels . . . . . . . . . . . . . . . . . . . . . . 225<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2.1 Intersection etsous-espace engendre par une partie . . . . . . . . . 225<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2.2 Somme desous-espaces vectoriels . . . . . . . . . . . . . . . . . . . 232<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2.3 Sommes directeset sous-espaces vectoriels suppl</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mentaires . . . . . 236<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.2.4 Produit cart</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">sien de deux espaces vectoriels . . . . . . . . . .. . . 241<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3 Sous-espacesaffines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3.1 Translations etgroupes des translations d<span lang="EN-US">’</span>un espace vectoriel . . . .243<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3.2 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition d<span lang="EN-US">’</span>un sous-espaceaffine . . . . . . . . . . . . . . . . . . . 244<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3.3 Parall</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">lisme . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 247<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.3.4 Intersection dedeux sous-espaces affines . . . . . . . . . . . . . . . 248<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4 Applications lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 249<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition et exemples . . . . . . . . . . . . . . .. . . . . . . . . . 249<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.2 Noyau et image d<span lang="EN-US">’</span>une application lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aire . . . . . .. . . . . . . . . 253<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.3 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">Equations lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires . . . . .. . . . . . . . . . . . . . . . . . . . . . 258<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.4 Ensembles desapplications lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">L</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">E,F</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">) . . . . . . . . . . . . . 259<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.5 Isomorphismes,automorphismes et groupe lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires . . . . . . . . . . 263<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.6 Restriction etrecollement . . . . . . . . . . . . . . . . . . . . . . . 265<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.7 Hyperplans d<span lang="EN-US">’</span>un espace vectoriel et formes lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires . . . . . . . . . 268<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.8 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">Etude d<span lang="EN-US">’</span>applications lin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aires remarquables . . . . . . . . . . . . . 271<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.8.a Homoth</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ties . . . . . . . . . . . . . . . . . . . . . . .. . 271<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.8.b Projecteurs .. . . . . . . . . . . . . . . . . . . . . . . . . 272<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.4.8.c Sym</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">tries . . . . . . . . . . . . . . . . . . . . . . .. . . . 276<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">4.5 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 5 Arithmétique dans </span></b><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">287<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1 Arithm</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">tique dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 288<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.1 Diviseurs etcongruences . . . . . . . . . . . . . . . . . . . . . . . . 288<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.2 Nombres premierset d</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">composition en produit de facteurs premiers 291<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.3 Divisioneuclidienne . . . . . . . . . . . . . . . . . . . . . . . . . . . 294<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.4 Sous-groupes de(</span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">,</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">+) .. . . . . . . . . . . . . . . . . . . . . . . . 295<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.5 Plus grandcommun diviseur et plus petit commun multiple . . . . 296<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.6 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de B</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">zout etalgorithme d<span lang="EN-US">’</span>Euclide . . . . . . . . . . . . . 298<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.1.7 Lemme d<span lang="EN-US">’</span>Euclide et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de Gauss . .. . . . . . . . . . . . . . 302<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.2 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.3 Annexe . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.3.1 Anneaux </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">/n</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et quelques propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s . . . . . . . . . . . . . . . . . 310<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">5.3.2 Corps </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">/p</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">et </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">l</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mentsinversibles de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">/n</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">Z </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">. . . . . . . . . . . . . 312<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 6 Fonctions r´eelles ou complexes d’unevariable réelle 313<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1 G</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ralit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s sur lesfonctions d<span lang="EN-US">’</span>une variable r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">elle . . . . . . . . . . . . . . . 314<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.1 Ensemble </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">F</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">I,</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">)et relation d<span lang="EN-US">’</span>ordre . . . . . . . . . . . . . . . . .314<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.2 Ensemble </span><i><span style="font-size:9.5pt;font-family:CMSY10;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMSY10">B</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">I,</span></i><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">). . . . . . . . . . . . . . . . . . . . . . . . . . . . 315<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.3 Fonctions p</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">riodiques . . . . . . . . . . . . . . . . . . . . .. . . . . 317<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.4 Fonctions paireset fonctions impaires . . . . . . . . . . . . . . . . . 318<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.5 Fonctionslipschitziennes . . . . . . . . . . . . . . . . . . . . . . . . 320<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.1.6 Fonctionsmonotones . . . . . . . . . . . . . . . . . . . . . . . . . . 322<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">Etude locale d<span lang="EN-US">’</span>une fonction. . . . . . . . . . . . . . . . . . . . . . . . . . 323<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.1 Voisinage d<span lang="EN-US">’</span>un point . . . . . . . . . . . . . . . . . . . . . . . . . .323<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.2 Limite d<span lang="EN-US">’</span>une fonction en un point et continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> en un point . . . . . 325<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.3 Operations alg</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">briques sur les limites . . . . . . . . . . . . . .. . . 335<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.4 Compatibilit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> du passage </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> la limite avecla relation d<span lang="EN-US">’</span>ordre dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">341<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.5 Composition delimites et caract</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">risation s</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quentiellede la limite . 348<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.2.6 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de la limite monotone . . . . . . . . . .. . . . . . . . . . 353<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3 Relations decomparaisons . . . . . . . . . . . . . . . . . . . . . . . . . . . 356<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3.1 Fonctions domin</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">es et fonctions n</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gligeablespar rapport `a une autre<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">au voisinage d<span lang="EN-US">’</span>un point . . . . . . . . . . . . . . . . . . . . . . . . .356<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3.2 Comparaison desfonctions usuelles . . . . . . . . . . . . . . . . . . 363<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3.3 Fonctions </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quivalentes en un point . . . . . . . . . . . . . .. . . . 364<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.3.4 Equivalentsusuels . . . . . . . . . . . . . . . . . . . . . . . . . . . 368<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4 Continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> globale . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 372<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition et premi7res propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s . . . . . . . . . . . . . . . . . . . 372<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.2 Compos</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">e de deux fonctions continues . . . . . . . . . . .. . . . . 374<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.3 Restriction et caract</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">re </span><span style="font-size:9.5pt;font-family:LMRoman12-Regular;mso-bidi-font-family:LMRoman12-Regular">« </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">local </span><span style="font-size:9.5pt;font-family:LMRoman12-Regular;mso-bidi-font-family:LMRoman12-Regular">» </span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">de la continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> . . . . . . . .. . . 375<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.4 Prolongement parcontinuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> . . . . . . . . . . . . . . . . . . . . . . 376<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.5 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me des valeurs interm</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">diaires . . . . . . . . . . . . . . . . . 378<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.6 Image d<span lang="EN-US">’</span>un segment par une fonction continue . . . . . . . . . . . .381<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.7 Continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> de la bijection r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ciproque. . . . . . . . . . . . . . . . . 383<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.4.8 Continuit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> uniforme et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de Heine . . . . . . . . . . . . . . 384<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.5 Bilan sur les diff</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rences entre fonctions `a valeurs r</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">elles ou complexes . . . 389<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">6.6 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><b><span style="font-size:9.5pt;font-family:CMBX12;mso-bidi-font-family:CMBX12">Chapitre 7 Polynômes et fractions rationnelles 396<o:p></o:p></span></b></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 397<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1.1 Alg</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">bres et morphisme d<span lang="EN-US">’</span>alg</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">bres . . . . . . . . . . . . . . . . . . . 397<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1.2 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition d<span lang="EN-US">’</span>un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . . . . . . . . . . .401<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1.3 Operationsusuelles sur les polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes . . . . . . . . . . . . . . . . . 401<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.1.4 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rivation sur l<span lang="EN-US">’</span>ensemble despolyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes . . . . . . . . . . . . . . . 409<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.2 Degr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> d<span lang="EN-US">’</span>un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 412<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.2.1 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">finition . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 412<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.2.2 Propri</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">t</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">s du degr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> . . . . . . . .. . . . . . . . . . . . . . . . . . . 413<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.2.3 Cons</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">quences fondamentales . . . . . . . . . . . . . . .. . . . . . . 414<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3 Arithm</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">tique dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] .. . . . . . . . . . . . . . . . . . . . . . . . . . . 415<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.1 Divisibilit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] .. . . . . . . . . . . . . . . . . . . . . . . . 415<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.2 Divisioneuclidienne dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] .. . . . . . . . . . . . . . . . . . . 419<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.3 Id</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">aux de </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 423<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.4 Polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes premiers entre eux . . . . . . . . . . . . . .. . . . . . . 425<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.3.5 Th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de B</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">zout et th</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">or</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">è</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me de Gauss . . . . . . . . . . . . . . 427<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4 Racines d<span lang="EN-US">’</span>un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 429<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.1 Fonctionpolynomiale associ</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">e </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">à</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . 429<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.2 Racines d<span lang="EN-US">’</span>un polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">me . . . . . . . . . . . . . . . . . . . . .. . . . 430<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.3 Formule deTaylor et multiplicit</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> d<span lang="EN-US">’</span>une racine . . .. . . . . . . . . 432<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.4 M</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">thodes pour montrer que deux polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes sont </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">gaux . . . . . .436<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.4.5 Polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes scindes et relations entre racines etcoefficients . . . . . 437<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.5 Polyn</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">mes irr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ductibles etfactorisation . . . . . . . . . . . . . . . . . . . . 439<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.5.1 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">El</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ments irr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ductibles dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">C</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] . . . . . . . . . . . . . . . . . . . 440<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.5.2 </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">´</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">El</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ments irr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ductibles dans </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">R</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">[</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">] . . . . . . . . . . . . . . . . . . . 441<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6 Ensemble </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">) . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 442<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6.1 Corps desfractions rationnelles </span><span style="font-size:9.5pt;font-family:MSBM10;mso-bidi-font-family:MSBM10">K</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">(</span><i><span style="font-size:9.5pt;font-family:CMMI12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMMI12">X</span></i><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">) .. . . . . . . . . . . . . . . . 442<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6.2 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">rivation et degr</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12"> . . . . . . . .. . . . . . . . . . . . . . . . . . . 443<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6.3 Z</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ros et p</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">ô</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">les d<span lang="EN-US">’</span>une fraction rationnelle . . . . . . . . . . . . . . . . 445<o:p></o:p></span></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.6.4 D</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">composition en </span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">l</span><span style="font-size:9.5pt;font-family:CMBX12;mso-ascii-font-family:CMR12;mso-fareast-font-family:CMR12;mso-bidi-font-family:CMR12">é</span><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">ments simples . . . . . . . . . . . . . . . . . .446<o:p></o:p></span></p><p></p><p class="MsoNormal" style="margin-bottom:0cm;line-height:normal;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:9.5pt;font-family:CMR12;mso-hansi-font-family:CMBX12;mso-bidi-font-family:CMR12">7.7 Exercices . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448<o:p></o:p></span></p>
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