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</header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Sommaire" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Sommaire</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">déplacer vers la barre latérale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">masquer</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Début</div> </a> </li> <li id="toc-Motivation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Motivation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Motivation</span> </div> </a> <ul id="toc-Motivation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fragments_d'histoire" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fragments_d'histoire"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Fragments d'histoire</span> </div> </a> <ul id="toc-Fragments_d'histoire-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Règles_opératoires" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Règles_opératoires"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Règles opératoires</span> </div> </a> <button aria-controls="toc-Règles_opératoires-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Règles opératoires</span> </button> <ul id="toc-Règles_opératoires-sublist" class="vector-toc-list"> <li id="toc-Addition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Addition"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Addition</span> </div> </a> <ul id="toc-Addition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Multiplication" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Multiplication"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Multiplication</span> </div> </a> <ul id="toc-Multiplication-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ensemble_des_entiers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ensemble_des_entiers"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Ensemble des entiers</span> </div> </a> <button aria-controls="toc-Ensemble_des_entiers-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Ensemble des entiers</span> </button> <ul id="toc-Ensemble_des_entiers-sublist" class="vector-toc-list"> <li id="toc-Construction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Construction"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Construction</span> </div> </a> <ul id="toc-Construction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Structure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Structure"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Structure</span> </div> </a> <ul id="toc-Structure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Extensions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Extensions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Extensions</span> </div> </a> <ul id="toc-Extensions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Utilisations_courantes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Utilisations_courantes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Utilisations courantes</span> </div> </a> <ul id="toc-Utilisations_courantes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_et_références" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_et_références"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes et références</span> </div> </a> <ul id="toc-Notes_et_références-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voir_aussi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voir_aussi"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Voir aussi</span> </div> </a> <ul id="toc-Voir_aussi-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sommaire" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Basculer la table des matières" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Basculer la table des matières</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Entier relatif</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Aller à un article dans une autre langue. Disponible en 131 langues." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-131" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">131 langues</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Heelgetal" title="Heelgetal – afrikaans" lang="af" hreflang="af" data-title="Heelgetal" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Ganze_Zahl" title="Ganze Zahl – alémanique" lang="gsw" hreflang="gsw" data-title="Ganze Zahl" data-language-autonym="Alemannisch" data-language-local-name="alémanique" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Numero_entero" title="Numero entero – aragonais" lang="an" hreflang="an" data-title="Numero entero" data-language-autonym="Aragonés" data-language-local-name="aragonais" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%AA%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="पूर्ण संख्या – angika" lang="anp" hreflang="anp" data-title="पूर्ण संख्या" data-language-autonym="अंगिका" data-language-local-name="angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%B5%D8%AD%D9%8A%D8%AD" title="عدد صحيح – arabe" lang="ar" hreflang="ar" data-title="عدد صحيح" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%85%E0%A6%96%E0%A6%A3%E0%A7%8D%E0%A6%A1_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="অখণ্ড সংখ্যা – assamais" lang="as" hreflang="as" data-title="অখণ্ড সংখ্যা" data-language-autonym="অসমীয়া" data-language-local-name="assamais" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/N%C3%BAmberu_enteru" title="Númberu enteru – asturien" lang="ast" hreflang="ast" data-title="Númberu enteru" data-language-autonym="Asturianu" data-language-local-name="asturien" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Tam_%C9%99d%C9%99dl%C9%99r" title="Tam ədədlər – azerbaïdjanais" lang="az" hreflang="az" data-title="Tam ədədlər" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaïdjanais" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AA%D8%A7%D9%85_%D8%B3%D8%A7%DB%8C%DB%8C%D9%84%D8%A7%D8%B1" title="تام ساییلار – South Azerbaijani" lang="azb" hreflang="azb" data-title="تام ساییلار" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%91%D3%A9%D1%82%D3%A9%D0%BD_%D2%BB%D0%B0%D0%BD" title="Бөтөн һан – bachkir" lang="ba" hreflang="ba" data-title="Бөтөн һан" data-language-autonym="Башҡортса" data-language-local-name="bachkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Sv%C4%93kas%C4%97s_skaitlios" title="Svēkasės skaitlios – samogitien" lang="sgs" hreflang="sgs" data-title="Svēkasės skaitlios" data-language-autonym="Žemaitėška" data-language-local-name="samogitien" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Integer" title="Integer – Central Bikol" lang="bcl" hreflang="bcl" data-title="Integer" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A6%D1%8D%D0%BB%D1%8B_%D0%BB%D1%96%D0%BA" title="Цэлы лік – biélorusse" lang="be" hreflang="be" data-title="Цэлы лік" data-language-autonym="Беларуская" data-language-local-name="biélorusse" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A6%D1%8D%D0%BB%D1%8B_%D0%BB%D1%96%D0%BA" title="Цэлы лік – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Цэлы лік" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A6%D1%8F%D0%BB%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Цяло число – bulgare" lang="bg" hreflang="bg" data-title="Цяло число" data-language-autonym="Български" data-language-local-name="bulgare" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%82%E0%A6%B0%E0%A7%8D%E0%A6%A3_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="পূর্ণ সংখ্যা – bengali" lang="bn" hreflang="bn" data-title="পূর্ণ সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Kevan_daveel" title="Kevan daveel – breton" lang="br" hreflang="br" data-title="Kevan daveel" data-language-autonym="Brezhoneg" data-language-local-name="breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Cijeli_broj" title="Cijeli broj – bosniaque" lang="bs" hreflang="bs" data-title="Cijeli broj" data-language-autonym="Bosanski" data-language-local-name="bosniaque" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_enter" title="Nombre enter – catalan" lang="ca" hreflang="ca" data-title="Nombre enter" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95%DB%8C_%D8%AA%DB%95%D9%88%D8%A7%D9%88" title="ژمارەی تەواو – sorani" lang="ckb" hreflang="ckb" data-title="ژمارەی تەواو" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Cel%C3%A9_%C4%8D%C3%ADslo" title="Celé číslo – tchèque" lang="cs" hreflang="cs" data-title="Celé číslo" data-language-autonym="Čeština" data-language-local-name="tchèque" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D1%83%D0%BB%D0%BB%D0%B8_%D1%85%D0%B8%D1%81%D0%B5%D0%BF" title="Тулли хисеп – tchouvache" lang="cv" hreflang="cv" data-title="Тулли хисеп" data-language-autonym="Чӑвашла" data-language-local-name="tchouvache" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cyfanrif" title="Cyfanrif – gallois" lang="cy" hreflang="cy" data-title="Cyfanrif" data-language-autonym="Cymraeg" data-language-local-name="gallois" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Heltal" title="Heltal – danois" lang="da" hreflang="da" data-title="Heltal" data-language-autonym="Dansk" data-language-local-name="danois" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Ganze_Zahl" title="Ganze Zahl – allemand" lang="de" hreflang="de" data-title="Ganze Zahl" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BA%CE%AD%CF%81%CE%B1%CE%B9%CE%BF%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82" title="Ακέραιος αριθμός – grec" lang="el" hreflang="el" data-title="Ακέραιος αριθμός" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Integer" title="Integer – anglais" lang="en" hreflang="en" data-title="Integer" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Entjero" title="Entjero – espéranto" lang="eo" hreflang="eo" data-title="Entjero" data-language-autonym="Esperanto" data-language-local-name="espéranto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_entero" title="Número entero – espagnol" lang="es" hreflang="es" data-title="Número entero" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/T%C3%A4isarv" title="Täisarv – estonien" lang="et" hreflang="et" data-title="Täisarv" data-language-autonym="Eesti" data-language-local-name="estonien" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki_oso" title="Zenbaki oso – basque" lang="eu" hreflang="eu" data-title="Zenbaki oso" data-language-autonym="Euskara" data-language-local-name="basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%B5%D8%AD%DB%8C%D8%AD" title="عدد صحیح – persan" lang="fa" hreflang="fa" data-title="عدد صحیح" data-language-autonym="فارسی" data-language-local-name="persan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kokonaisluku" title="Kokonaisluku – finnois" lang="fi" hreflang="fi" data-title="Kokonaisluku" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Terveharv" title="Terveharv – võro" lang="vro" hreflang="vro" data-title="Terveharv" data-language-autonym="Võro" data-language-local-name="võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Integer" title="Integer – fidjien" lang="fj" hreflang="fj" data-title="Integer" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fidjien" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Heiltal" title="Heiltal – féroïen" lang="fo" hreflang="fo" data-title="Heiltal" data-language-autonym="Føroyskt" data-language-local-name="féroïen" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Hial_taal" title="Hial taal – frison septentrional" lang="frr" hreflang="frr" data-title="Hial taal" data-language-autonym="Nordfriisk" data-language-local-name="frison septentrional" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Sl%C3%A1nuimhir" title="Slánuimhir – irlandais" lang="ga" hreflang="ga" data-title="Slánuimhir" data-language-autonym="Gaeilge" data-language-local-name="irlandais" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%95%B4%E6%95%B8" title="整數 – gan" lang="gan" hreflang="gan" data-title="整數" data-language-autonym="贛語" data-language-local-name="gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Anty%C3%A9_r%C3%A9latif" title="Antyé rélatif – créole guyanais" lang="gcr" hreflang="gcr" data-title="Antyé rélatif" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="créole guyanais" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%BAmero_enteiro" title="Número enteiro – galicien" lang="gl" hreflang="gl" data-title="Número enteiro" data-language-autonym="Galego" data-language-local-name="galicien" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AA%E0%AB%82%E0%AA%B0%E0%AB%8D%E0%AA%A3%E0%AA%BE%E0%AA%82%E0%AA%95_%E0%AA%B8%E0%AA%82%E0%AA%96%E0%AB%8D%E0%AA%AF%E0%AA%BE%E0%AA%93" title="પૂર્ણાંક સંખ્યાઓ – goudjarati" lang="gu" hreflang="gu" data-title="પૂર્ણાંક સંખ્યાઓ" data-language-autonym="ગુજરાતી" data-language-local-name="goudjarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/Helu_piha" title="Helu piha – hawaïen" lang="haw" hreflang="haw" data-title="Helu piha" data-language-autonym="Hawaiʻi" data-language-local-name="hawaïen" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%A9%D7%9C%D7%9D" title="מספר שלם – hébreu" lang="he" hreflang="he" data-title="מספר שלם" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3%E0%A4%BE%E0%A4%82%E0%A4%95" title="पूर्णांक – hindi" lang="hi" hreflang="hi" data-title="पूर्णांक" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Cijeli_broj" title="Cijeli broj – croate" lang="hr" hreflang="hr" data-title="Cijeli broj" data-language-autonym="Hrvatski" data-language-local-name="croate" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Cy%C5%82a_li%C4%8Dba" title="Cyła ličba – haut-sorabe" lang="hsb" hreflang="hsb" data-title="Cyła ličba" data-language-autonym="Hornjoserbsce" data-language-local-name="haut-sorabe" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Eg%C3%A9sz_sz%C3%A1mok" title="Egész számok – hongrois" lang="hu" hreflang="hu" data-title="Egész számok" data-language-autonym="Magyar" data-language-local-name="hongrois" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B4%D5%A2%D5%B8%D5%B2%D5%BB_%D5%A9%D5%AB%D5%BE" title="Ամբողջ թիվ – arménien" lang="hy" hreflang="hy" data-title="Ամբողջ թիվ" data-language-autonym="Հայերեն" data-language-local-name="arménien" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B1%D5%B4%D5%A2%D5%B8%D5%B2%D5%BB_%D5%A9%D5%AB%D6%82" title="Ամբողջ թիւ – arménien occidental" lang="hyw" hreflang="hyw" data-title="Ամբողջ թիւ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="arménien occidental" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Numero_integre" title="Numero integre – interlingua" lang="ia" hreflang="ia" data-title="Numero integre" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Integer" title="Integer – iban" lang="iba" hreflang="iba" data-title="Integer" data-language-autonym="Jaku Iban" data-language-local-name="iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan_bulat" title="Bilangan bulat – indonésien" lang="id" hreflang="id" data-title="Bilangan bulat" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%91%D3%80%D0%B0%D1%80%D1%87%D1%87%D0%B0_%D1%82%D0%B0%D1%8C%D1%80%D0%B0%D1%85%D1%8C" title="БӀарчча таьрахь – ingouche" lang="inh" hreflang="inh" data-title="БӀарчча таьрахь" data-language-autonym="ГӀалгӀай" data-language-local-name="ingouche" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Integro" title="Integro – ido" lang="io" hreflang="io" data-title="Integro" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Heilt%C3%B6lur" title="Heiltölur – islandais" lang="is" hreflang="is" data-title="Heiltölur" data-language-autonym="Íslenska" data-language-local-name="islandais" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_intero" title="Numero intero – italien" lang="it" hreflang="it" data-title="Numero intero" data-language-autonym="Italiano" data-language-local-name="italien" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%95%B4%E6%95%B0" title="整数 – japonais" lang="ja" hreflang="ja" data-title="整数" data-language-autonym="日本語" data-language-local-name="japonais" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Intiga" title="Intiga – créole jamaïcain" lang="jam" hreflang="jam" data-title="Intiga" data-language-autonym="Patois" data-language-local-name="créole jamaïcain" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/mulna%27u" title="mulna'u – lojban" lang="jbo" hreflang="jbo" data-title="mulna'u" data-language-autonym="La .lojban." data-language-local-name="lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Wilangan_bulat" title="Wilangan bulat – javanais" lang="jv" hreflang="jv" data-title="Wilangan bulat" data-language-autonym="Jawa" data-language-local-name="javanais" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%97%E1%83%94%E1%83%9A%E1%83%98_%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%98" title="მთელი რიცხვი – géorgien" lang="ka" hreflang="ka" data-title="მთელი რიცხვი" data-language-autonym="ქართული" data-language-local-name="géorgien" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D2%AF%D1%82%D1%96%D0%BD_%D1%81%D0%B0%D0%BD" title="Бүтін сан – kazakh" lang="kk" hreflang="kk" data-title="Бүтін сан" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%95%EC%88%98" title="정수 – coréen" lang="ko" hreflang="ko" data-title="정수" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Tamhejmar" title="Tamhejmar – kurde" lang="ku" hreflang="ku" data-title="Tamhejmar" data-language-autonym="Kurdî" data-language-local-name="kurde" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D2%AF%D1%82%D2%AF%D0%BD_%D1%81%D0%B0%D0%BD%D0%B4%D0%B0%D1%80" title="Бүтүн сандар – kirghize" lang="ky" hreflang="ky" data-title="Бүтүн сандар" data-language-autonym="Кыргызча" data-language-local-name="kirghize" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numerus_integer" title="Numerus integer – latin" lang="la" hreflang="la" data-title="Numerus integer" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Ganz_Zuel" title="Ganz Zuel – luxembourgeois" lang="lb" hreflang="lb" data-title="Ganz Zuel" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxembourgeois" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Numero_intera" title="Numero intera – lingua franca nova" lang="lfn" hreflang="lfn" data-title="Numero intera" data-language-autonym="Lingua Franca Nova" data-language-local-name="lingua franca nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Gans_getal" title="Gans getal – limbourgeois" lang="li" hreflang="li" data-title="Gans getal" data-language-autonym="Limburgs" data-language-local-name="limbourgeois" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Numer_intreg" title="Numer intreg – lombard" lang="lmo" hreflang="lmo" data-title="Numer intreg" data-language-autonym="Lombard" data-language-local-name="lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%88%E0%BA%B3%E0%BA%99%E0%BA%A7%E0%BA%99%E0%BA%96%E0%BB%89%E0%BA%A7%E0%BA%99" title="ຈຳນວນຖ້ວນ – lao" lang="lo" hreflang="lo" data-title="ຈຳນວນຖ້ວນ" data-language-autonym="ລາວ" data-language-local-name="lao" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Sveikasis_skai%C4%8Dius" title="Sveikasis skaičius – lituanien" lang="lt" hreflang="lt" data-title="Sveikasis skaičius" data-language-autonym="Lietuvių" data-language-local-name="lituanien" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Vesels_skaitlis" title="Vesels skaitlis – letton" lang="lv" hreflang="lv" data-title="Vesels skaitlis" data-language-autonym="Latviešu" data-language-local-name="letton" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Isa_tsimivaky" title="Isa tsimivaky – malgache" lang="mg" hreflang="mg" data-title="Isa tsimivaky" data-language-autonym="Malagasy" data-language-local-name="malgache" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BB_%D0%B1%D1%80%D0%BE%D1%98" title="Цел број – macédonien" lang="mk" hreflang="mk" data-title="Цел број" data-language-autonym="Македонски" data-language-local-name="macédonien" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%82%E0%B5%BC%E0%B4%A3%E0%B5%8D%E0%B4%A3%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF" title="പൂർണ്ണസംഖ്യ – malayalam" lang="ml" hreflang="ml" data-title="പൂർണ്ണസംഖ്യ" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%91%D2%AF%D1%85%D1%8D%D0%BB_%D1%82%D0%BE%D0%BE" title="Бүхэл тоо – mongol" lang="mn" hreflang="mn" data-title="Бүхэл тоо" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="पूर्ण संख्या – marathi" lang="mr" hreflang="mr" data-title="पूर्ण संख्या" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Integer" title="Integer – malais" lang="ms" hreflang="ms" data-title="Integer" data-language-autonym="Bahasa Melayu" data-language-local-name="malais" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Integer" title="Integer – maltais" lang="mt" hreflang="mt" data-title="Integer" data-language-autonym="Malti" data-language-local-name="maltais" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/N%C3%BAmaro_anteiro" title="Númaro anteiro – mirandais" lang="mwl" hreflang="mwl" data-title="Númaro anteiro" data-language-autonym="Mirandés" data-language-local-name="mirandais" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Hele_Tall" title="Hele Tall – bas-allemand" lang="nds" hreflang="nds" data-title="Hele Tall" data-language-autonym="Plattdüütsch" data-language-local-name="bas-allemand" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Geheel_getal" title="Geheel getal – néerlandais" lang="nl" hreflang="nl" data-title="Geheel getal" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Heiltal" title="Heiltal – norvégien nynorsk" lang="nn" hreflang="nn" data-title="Heiltal" data-language-autonym="Norsk nynorsk" data-language-local-name="norvégien nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Heltall" title="Heltall – norvégien bokmål" lang="nb" hreflang="nb" data-title="Heltall" data-language-autonym="Norsk bokmål" data-language-local-name="norvégien bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nso mw-list-item"><a href="https://nso.wikipedia.org/wiki/Integer" title="Integer – sotho du Nord" lang="nso" hreflang="nso" data-title="Integer" data-language-autonym="Sesotho sa Leboa" data-language-local-name="sotho du Nord" class="interlanguage-link-target"><span>Sesotho sa Leboa</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Nombre_enti%C3%A8r" title="Nombre entièr – occitan" lang="oc" hreflang="oc" data-title="Nombre entièr" data-language-autonym="Occitan" data-language-local-name="occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Lakkoofsa_Intiijarii" title="Lakkoofsa Intiijarii – oromo" lang="om" hreflang="om" data-title="Lakkoofsa Intiijarii" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A9%82%E0%A8%B0%E0%A8%A8_%E0%A8%B8%E0%A9%B0%E0%A8%96%E0%A8%BF%E0%A8%86" title="ਪੂਰਨ ਸੰਖਿਆ – pendjabi" lang="pa" hreflang="pa" data-title="ਪੂਰਨ ਸੰਖਿਆ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pendjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczby_ca%C5%82kowite" title="Liczby całkowite – polonais" lang="pl" hreflang="pl" data-title="Liczby całkowite" data-language-autonym="Polski" data-language-local-name="polonais" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/N%C3%B9mer_antregh" title="Nùmer antregh – piémontais" lang="pms" hreflang="pms" data-title="Nùmer antregh" data-language-autonym="Piemontèis" data-language-local-name="piémontais" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%86%D9%B9%DB%8C%D8%AC%D8%B1" title="انٹیجر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انٹیجر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero_inteiro" title="Número inteiro – portugais" lang="pt" hreflang="pt" data-title="Número inteiro" data-language-autonym="Português" data-language-local-name="portugais" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_%C3%AEntreg" title="Număr întreg – roumain" lang="ro" hreflang="ro" data-title="Număr întreg" data-language-autonym="Română" data-language-local-name="roumain" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437798 badge-goodarticle mw-list-item" title="bon article"><a href="https://ru.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BB%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Целое число – russe" lang="ru" hreflang="ru" data-title="Целое число" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/N%C3%B9mmuru_rilativu" title="Nùmmuru rilativu – sicilien" lang="scn" hreflang="scn" data-title="Nùmmuru rilativu" data-language-autonym="Sicilianu" data-language-local-name="sicilien" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Cijeli_broj" title="Cijeli broj – serbo-croate" lang="sh" hreflang="sh" data-title="Cijeli broj" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croate" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B1%E0%B7%92%E0%B6%9B%E0%B7%92%E0%B6%BD" title="නිඛිල – cingalais" lang="si" hreflang="si" data-title="නිඛිල" data-language-autonym="සිංහල" data-language-local-name="cingalais" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Integer" title="Integer – Simple English" lang="en-simple" hreflang="en-simple" data-title="Integer" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Cel%C3%A9_%C4%8D%C3%ADslo" title="Celé číslo – slovaque" lang="sk" hreflang="sk" data-title="Celé číslo" data-language-autonym="Slovenčina" data-language-local-name="slovaque" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Celo_%C5%A1tevilo" title="Celo število – slovène" lang="sl" hreflang="sl" data-title="Celo število" data-language-autonym="Slovenščina" data-language-local-name="slovène" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Nhamba_mhumburu" title="Nhamba mhumburu – shona" lang="sn" hreflang="sn" data-title="Nhamba mhumburu" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Abyoone" title="Abyoone – somali" lang="so" hreflang="so" data-title="Abyoone" data-language-autonym="Soomaaliga" data-language-local-name="somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Numrat_e_plot%C3%AB" title="Numrat e plotë – albanais" lang="sq" hreflang="sq" data-title="Numrat e plotë" data-language-autonym="Shqip" data-language-local-name="albanais" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BE_%D0%B1%D1%80%D0%BE%D1%98" title="Цео број – serbe" lang="sr" hreflang="sr" data-title="Цео број" data-language-autonym="Српски / srpski" data-language-local-name="serbe" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Heltal" title="Heltal – suédois" lang="sv" hreflang="sv" data-title="Heltal" data-language-autonym="Svenska" data-language-local-name="suédois" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Nambakamili" title="Nambakamili – swahili" lang="sw" hreflang="sw" data-title="Nambakamili" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Co%C5%82kowito_n%C5%AFmera" title="Cołkowito nůmera – silésien" lang="szl" hreflang="szl" data-title="Cołkowito nůmera" data-language-autonym="Ślůnski" data-language-local-name="silésien" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%B4%E0%AF%81_%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="முழு எண் – tamoul" lang="ta" hreflang="ta" data-title="முழு எண்" data-language-autonym="தமிழ்" data-language-local-name="tamoul" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AA%E0%B1%82%E0%B0%B0%E0%B1%8D%E0%B0%A3_%E0%B0%B8%E0%B0%82%E0%B0%96%E0%B1%8D%E0%B0%AF" title="పూర్ణ సంఖ్య – télougou" lang="te" hreflang="te" data-title="పూర్ణ సంఖ్య" data-language-autonym="తెలుగు" data-language-local-name="télougou" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%B4%D0%B0%D0%B4%D2%B3%D0%BE%D0%B8_%D0%B1%D1%83%D1%82%D1%83%D0%BD" title="Ададҳои бутун – tadjik" lang="tg" hreflang="tg" data-title="Ададҳои бутун" data-language-autonym="Тоҷикӣ" data-language-local-name="tadjik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="จำนวนเต็ม – thaï" lang="th" hreflang="th" data-title="จำนวนเต็ม" data-language-autonym="ไทย" data-language-local-name="thaï" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Bitin_sanlar" title="Bitin sanlar – turkmène" lang="tk" hreflang="tk" data-title="Bitin sanlar" data-language-autonym="Türkmençe" data-language-local-name="turkmène" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Buumbilang" title="Buumbilang – tagalog" lang="tl" hreflang="tl" data-title="Buumbilang" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Tam_say%C4%B1" title="Tam sayı – turc" lang="tr" hreflang="tr" data-title="Tam sayı" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A6%D1%96%D0%BB%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Ціле число – ukrainien" lang="uk" hreflang="uk" data-title="Ціле число" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B5%D8%AD%DB%8C%D8%AD_%D8%B9%D8%AF%D8%AF" title="صحیح عدد – ourdou" lang="ur" hreflang="ur" data-title="صحیح عدد" data-language-autonym="اردو" data-language-local-name="ourdou" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Butun_sonlar" title="Butun sonlar – ouzbek" lang="uz" hreflang="uz" data-title="Butun sonlar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ouzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91_nguy%C3%AAn" title="Số nguyên – vietnamien" lang="vi" hreflang="vi" data-title="Số nguyên" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamien" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Geh%C3%AAel_getal" title="Gehêel getal – flamand occidental" lang="vls" hreflang="vls" data-title="Gehêel getal" data-language-autonym="West-Vlams" data-language-local-name="flamand occidental" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Buok" title="Buok – waray" lang="war" hreflang="war" data-title="Buok" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%95%B4%E6%95%B0" title="整数 – wu" lang="wuu" hreflang="wuu" data-title="整数" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%91%D2%AF%D0%BA%D0%BB_%D1%82%D0%BE%D0%B9%D0%B3" title="Бүкл тойг – kalmouk" lang="xal" hreflang="xal" data-title="Бүкл тойг" data-language-autonym="Хальмг" data-language-local-name="kalmouk" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-integer" title="I-integer – xhosa" lang="xh" hreflang="xh" data-title="I-integer" data-language-autonym="IsiXhosa" data-language-local-name="xhosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%92%D7%90%D7%A0%D7%A6%D7%A2_%D7%A6%D7%90%D7%9C" title="גאנצע צאל – yiddish" lang="yi" hreflang="yi" data-title="גאנצע צאל" data-language-autonym="ייִדיש" data-language-local-name="yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/N%E1%BB%8D%CC%81mb%C3%A0_odidi" title="Nọ́mbà odidi – yoruba" lang="yo" hreflang="yo" data-title="Nọ́mbà odidi" data-language-autonym="Yorùbá" data-language-local-name="yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%B4%E6%95%B0" title="整数 – chinois" lang="zh" hreflang="zh" data-title="整数" data-language-autonym="中文" data-language-local-name="chinois" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%95%B4%E6%95%B8" title="整數 – chinois littéraire" lang="lzh" hreflang="lzh" data-title="整數" data-language-autonym="文言" data-language-local-name="chinois littéraire" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ch%C3%A9ng-s%C3%B2%CD%98" title="Chéng-sò͘ – minnan" lang="nan" hreflang="nan" data-title="Chéng-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="minnan" 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mw-parser-output" lang="fr" dir="ltr"><div class="bandeau-container metadata homonymie hatnote"><div class="bandeau-cell bandeau-icone" style="display:table-cell;padding-right:0.5em"><span class="noviewer" typeof="mw:File"><a href="/wiki/Aide:Homonymie" title="Aide:Homonymie"><img alt="Page d’aide sur l’homonymie" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/20px-Logo_disambig.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/30px-Logo_disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/40px-Logo_disambig.svg.png 2x" data-file-width="512" data-file-height="375" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p>Pour les articles homonymes, voir <a href="/wiki/Entier" class="mw-disambig" title="Entier">Entier</a>. </p> </div></div> <p>En <a href="/wiki/Math%C3%A9matiques" title="Mathématiques">mathématiques</a>, un <b>entier relatif</b>, un <b>entier rationnel</b> ou simplement un <b>nombre entier</b> est un <a href="/wiki/Nombre" title="Nombre">nombre</a> qui se présente comme un <a href="/wiki/Entier_naturel" title="Entier naturel">entier naturel</a> auquel on a adjoint un <a href="/wiki/Signe_(arithm%C3%A9tique)" title="Signe (arithmétique)">signe</a> positif ou négatif indiquant sa position<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup> par rapport à <a href="/wiki/Z%C3%A9ro" title="Zéro">0</a> sur un axe orienté. Les entiers <a href="/wiki/Nombre_positif" title="Nombre positif">positifs</a> (supérieurs à zéro) s'identifient aux <a href="/wiki/Entiers_naturels" class="mw-redirect" title="Entiers naturels">entiers naturels</a> : 0, 1, 2, 3… tandis que les entiers <a href="/wiki/Nombre_n%C3%A9gatif" title="Nombre négatif">négatifs</a> sont leurs <a href="/wiki/Oppos%C3%A9_(math%C3%A9matiques)" title="Opposé (mathématiques)">opposés</a> : 0, −1, −2, −3… L'entier 0 lui-même est donc le seul nombre à la fois positif et négatif<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup>. </p><p>Un <a href="/wiki/Nombre_r%C3%A9el" title="Nombre réel">nombre réel</a> est entier s'il est sans <a href="/wiki/Partie_fractionnaire" class="mw-redirect" title="Partie fractionnaire">partie fractionnaire</a>, c'est-à-dire si son <a href="/wiki/D%C3%A9veloppement_d%C3%A9cimal" title="Développement décimal">écriture décimale</a> ne comprend pas de chiffre (autre que <a href="/wiki/Z%C3%A9ro" title="Zéro">zéro</a>) « après la virgule ». </p><p>Les entiers relatifs permettent d'exprimer la <i><a href="/wiki/Diff%C3%A9rence" title="Différence">différence</a></i> de deux entiers naturels quelconques. Entre autres significations de la différence, on peut citer la position sur un axe orienté par rapport à un point de référence (un axe à positions <i>discrètes</i>, c'est-à-dire discontinues) ; le déplacement depuis une position d'origine, dans un sens ou dans l'autre ; ou encore la variation d'une valeur entière, donc comptée en unités (variation positive pour un gain, négative pour une perte). </p><p>L'<a href="/wiki/Ensemble" title="Ensemble">ensemble</a> des entiers relatifs est noté<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup> « <b>Z</b> », lettre capitale <a href="/wiki/Graisse_(typographie)" title="Graisse (typographie)">grasse</a> dans les textes <a href="/wiki/Dactylographie" title="Dactylographie">dactylographiés</a>, peu à peu supplantée par la graphie manuscrite avec une barre oblique <a href="https://fr.wiktionary.org/wiki/ajourer" class="extiw" title="wikt:ajourer">ajourée</a> : « ℤ ». La présence d'un <a href="/wiki/Ast%C3%A9risque" title="Astérisque">astérisque</a> en <a href="/wiki/Exposant_(typographie)" title="Exposant (typographie)">exposant</a> (« <b>Z</b>* ») désigne l'ensemble des entiers relatifs non nuls. La notation « <b>Z</b><sup>−</sup> » désigne l'ensemble des entiers négatifs.<sup class="need_ref_tag" style="padding-left:2px;"><a href="/wiki/Aide:R%C3%A9f%C3%A9rence_n%C3%A9cessaire" title="Aide:Référence nécessaire">[<abbr class="abbr" title="référence">réf.</abbr> souhaitée]</a></sup> Il est plus rare de trouver la notation « <b>Z</b><sup>+</sup> », remplacée par la notation « <b>N</b> » des entiers naturels par identification. </p><p>Cet ensemble est (<a href="/wiki/Ordre_total" title="Ordre total">totalement</a>) <a href="/wiki/Ensemble_ordonn%C3%A9" class="mw-redirect" title="Ensemble ordonné">ordonné</a> pour la relation de comparaison usuelle héritée des entiers naturels. Il est aussi muni des opérations d'addition et de multiplication qui fondent la notion d'<a href="/wiki/Anneau_unitaire" title="Anneau unitaire">anneau</a> en <a href="/wiki/Alg%C3%A8bre" title="Algèbre">algèbre</a>. </p><p>Les entiers relatifs sont aussi appelés <b>entiers rationnels</b><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite_crochet">[</span>4<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite_crochet">[</span>5<span class="cite_crochet">]</span></a></sup>, appellation qui ne doit pas entraîner de confusion avec les <a href="/wiki/Nombres_rationnels" class="mw-redirect" title="Nombres rationnels">nombres rationnels</a> ou fractions. Cette dénomination vient de l'anglais <i><span class="lang-en" lang="en">rational integer</span></i>, et désigne un cas particulier d'<a href="/wiki/Entier_alg%C3%A9brique" title="Entier algébrique">entiers algébriques</a>, construit sur le <a href="/wiki/Corps_de_nombres" title="Corps de nombres">corps de nombres</a> des <a href="/wiki/Nombre_rationnel" title="Nombre rationnel">rationnels</a>. On trouve cette appellation chez <a href="/wiki/Nicolas_Bourbaki" title="Nicolas Bourbaki">Nicolas Bourbaki</a><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite_crochet">[</span>6<span class="cite_crochet">]</span></a></sup> et certains mathématiciens s'inscrivant dans le mouvement des <a href="/wiki/Math%C3%A9matiques_modernes" title="Mathématiques modernes">mathématiques modernes</a>, parmi lesquels <a href="/wiki/Georges_Papy" title="Georges Papy">Georges Papy</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Number-line.svg" class="mw-file-description"><img alt="La droite des nombres" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Number-line.svg/660px-Number-line.svg.png" decoding="async" width="660" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Number-line.svg/990px-Number-line.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Number-line.svg/1320px-Number-line.svg.png 2x" data-file-width="750" data-file-height="50" /></a><figcaption>La droite des nombres permet de représenter les entiers relatifs.</figcaption></figure> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Motivation">Motivation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=1" title="Modifier la section : Motivation" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=1" title="Modifier le code source de la section : Motivation"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La principale raison de l'introduction des <a href="/wiki/Nombre_n%C3%A9gatif" title="Nombre négatif">nombres négatifs</a> est la possibilité de résoudre toutes les équations de la forme : </p> <dl><dd><i>a</i> + <i>x</i> = <i>b</i>, où <i>x</i> est l'inconnue et <i>a</i> et <i>b</i> sont des paramètres.</dd></dl> <p>Dans l'ensemble des entiers naturels, seules certaines de ces équations ont une solution. </p> <dl><dd>5 + <i>x</i> = 8 si et seulement si <i>x</i> = 3</dd> <dd>9 + <i>x </i>= 4 n'a pas de solution dans l'ensemble des entiers naturels. Elle possède une solution dans l'ensemble des entiers relatifs qui est −5.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Fragments_d'histoire"><span id="Fragments_d.27histoire"></span>Fragments d'histoire</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=2" title="Modifier la section : Fragments d'histoire" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=2" title="Modifier le code source de la section : Fragments d'histoire"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La première allusion à des nombres négatifs apparaît dans des textes indiens comme <i>l'Arybhatiya</i> du mathématicien indien <a href="/wiki/%C3%82ryabhata" class="mw-redirect" title="Âryabhata">Âryabhata</a> (476-550) où sont définies les règles d'additions et de soustractions. Les nombres négatifs apparaissent alors comme représentant des dettes et les nombres positifs comme des recettes. Quelques siècles plus tard, dans les écrits du mathématicien perse <a href="/wiki/Abu_l-Wafa" title="Abu l-Wafa">Abu l-Wafa</a> (940-998), on voit apparaître des produits de nombres négatifs par des nombres positifs. Cependant le nombre reste encore attaché à des quantités physiques et le nombre négatif n'a guère de statut <i>légal</i>. <a href="/wiki/Abou_Jafar_Muhammad_Ibn_M%C5%ABsa_al-Khuw%C4%81rizm%C4%AB" class="mw-redirect" title="Abou Jafar Muhammad Ibn Mūsa al-Khuwārizmī">Al Khuwarizmi</a> (783-850) par exemple, dans son ouvrage <i>la Transposition et la réduction</i> préfère traiter 6 types d'équations du second degré au lieu d'envisager des soustractions. </p><p>En Europe les nombres relatifs apparaissent tardivement, on attribue en général à <a href="/wiki/Simon_Stevin" title="Simon Stevin">Simon Stevin</a> (1548-1620) la fameuse <a href="#Multiplication">règle des signes</a> pour le produit de deux entiers relatifs. <a href="/wiki/Jean_le_Rond_D%27Alembert" class="mw-redirect" title="Jean le Rond D'Alembert">D'Alembert</a> (1717-1783) lui-même dans l'<i><a href="/wiki/Encyclop%C3%A9die_ou_Dictionnaire_raisonn%C3%A9_des_sciences,_des_arts_et_des_m%C3%A9tiers" title="Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers">Encyclopédie</a></i> envisage le nombre relatif comme une idée dangereuse. </p> <blockquote> <p>« Il faut avouer qu'il n'est pas facile de fixer l'idée des quantités négatives, & que quelques habiles gens ont même contribué à l'embrouiller par les notions peu exactes qu'ils en ont données. Dire que la quantité négative est au-dessous du rien, c'est avancer une chose qui ne se peut pas concevoir. Ceux qui prétendent que 1 n'est pas comparable à −1<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite_crochet">[</span>7<span class="cite_crochet">]</span></a></sup>, & que le rapport entre 1 & −1 est différent du rapport entre −1 & 1, sont dans une double erreur […] Il n'y a donc point réellement & absolument de quantité négative isolée : −3 pris abstraitement ne présente à l'esprit aucune idée. » </p> </blockquote><p style="margin:-0.7em 0 0.3em 6em">— D'Alembert, <cite>Dictionnaire raisonné des sciences, des arts et des métiers, <a href="https://fr.wikisource.org/wiki/L%E2%80%99Encyclop%C3%A9die/1re_%C3%A9dition/N%C3%89GATIF" class="extiw" title="s:L’Encyclopédie/1re édition/NÉGATIF">vol. 11</a></cite></p> <p>Il faut attendre encore deux siècles et l'avènement du formalisme pour voir apparaître une <a href="/wiki/Construction_des_entiers_relatifs" title="Construction des entiers relatifs">construction formelle de l'ensemble des entiers relatifs</a> à partir de classes d'équivalence de couples d'entiers naturels. </p><p>C'est à <a href="/wiki/Richard_Dedekind" title="Richard Dedekind">Richard Dedekind</a> (1831-1916) que l'on doit cette construction. Lui-même utilisait la lettre <i>K</i> pour désigner l'ensemble des entiers relatifs. Plusieurs autres conventions ont eu cours, jusqu'à ce que <a href="/wiki/Nicolas_Bourbaki" title="Nicolas Bourbaki">Nicolas Bourbaki</a> popularise l'usage de la lettre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle \mathbb {Z} }"></span>, initiale de l'allemand <i>Zahlen</i> (nombres)<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite_crochet">[</span>8<span class="cite_crochet">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Règles_opératoires"><span id="R.C3.A8gles_op.C3.A9ratoires"></span>Règles opératoires</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=3" title="Modifier la section : Règles opératoires" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=3" title="Modifier le code source de la section : Règles opératoires"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dans un nombre relatif, on distingue le signe (+ ou −) et la <a href="/wiki/Valeur_absolue" title="Valeur absolue">valeur absolue</a> : −3 a pour valeur absolue 3. </p> <div class="mw-heading mw-heading3"><h3 id="Addition"><a href="/wiki/Addition" title="Addition">Addition</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=4" title="Modifier la section : Addition" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=4" title="Modifier le code source de la section : Addition"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La somme de deux entiers de même signe s'obtient en additionnant les deux valeurs absolues et en conservant le signe commun : </p> <dl><dd>(−3) + (−5) = −8, écriture que l'on abrège en −3 − 5 = −8, supprimant le signe opératoire +.</dd></dl> <p>La somme de deux entiers relatifs de signes contraires s'obtient en calculant la différence entre les deux valeurs absolues et en lui affectant le signe de l'entier ayant la plus grande valeur absolue : </p> <dl><dd>(+3) + (−5) = −2, écriture que l'on abrège en 3 − 5 = −2.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Multiplication"><a href="/wiki/Multiplication" title="Multiplication">Multiplication</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=5" title="Modifier la section : Multiplication" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=5" title="Modifier le code source de la section : Multiplication"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Le résultat d'une multiplication s'appelle un produit. Le produit de deux nombres relatifs de même signe est toujours positif (+) et s'obtient en effectuant le produit des valeurs absolues : </p> <dl><dd>(+3) × (+4) = +12 que l'on abrège en 3 × 4 = 12</dd> <dd>(−3) × (−7)= + 21 = 21</dd></dl> <p>(le + n'étant pas obligatoire si le produit n'est pas négatif) </p><p>Le produit de deux nombres relatifs de signes différents est toujours négatif (−) et s'obtient en effectuant le produit des valeurs absolues </p> <dl><dd>(+7) × (−4) = −28</dd></dl> <p><b>Règle des signes</b> </p> <dl><dd><b>plus</b> multiplié par <b>plus</b>, donne produit <b>plus</b>.</dd> <dd><b>moins</b> multiplié par <b>moins</b>, donne produit <b>plus</b></dd> <dd><b>moins</b> multiplié par <b>plus</b> ou <b>plus</b> multiplié par <b>moins</b> donne produit <b>moins</b></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Ensemble_des_entiers">Ensemble des entiers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=6" title="Modifier la section : Ensemble des entiers" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=6" title="Modifier le code source de la section : Ensemble des entiers"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Construction">Construction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=7" title="Modifier la section : Construction" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=7" title="Modifier le code source de la section : Construction"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'ensemble <b>Z</b> des entiers relatifs peut être vu comme le <a href="/wiki/Sym%C3%A9trisation" title="Symétrisation">symétrisé</a> du semi-anneau <b>N</b> des entiers naturels. </p> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Construction_des_entiers_relatifs" title="Construction des entiers relatifs">Construction des entiers relatifs</a>.</div></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Construction_blackboard_integers.jpg" class="mw-file-description"><img alt="Une représentation d'une construction des entiers relatifs." src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Construction_blackboard_integers.jpg/330px-Construction_blackboard_integers.jpg" decoding="async" width="330" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Construction_blackboard_integers.jpg/495px-Construction_blackboard_integers.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Construction_blackboard_integers.jpg/660px-Construction_blackboard_integers.jpg 2x" data-file-width="1920" data-file-height="1080" /></a><figcaption> Une représentation d'une construction des entiers relatifs. </figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Structure">Structure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=8" title="Modifier la section : Structure" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=8" title="Modifier le code source de la section : Structure"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'ensemble des entiers relatifs, muni de ses <a href="/wiki/Loi_de_composition" title="Loi de composition">lois</a> d'addition et de multiplication, est le prototype de la notion d'<a href="/wiki/Anneau_unitaire" title="Anneau unitaire">anneau</a>. Il s'agit même d'un <a href="/wiki/Anneau_euclidien" title="Anneau euclidien">anneau euclidien</a>, en référence à la <a href="/wiki/Division_euclidienne" title="Division euclidienne">division euclidienne</a>. Il est donc également <a href="/wiki/Anneau_principal" title="Anneau principal">principal</a> et <i>a fortiori</i> <a href="/wiki/Anneau_factoriel" title="Anneau factoriel">factoriel</a> et <a href="/wiki/Anneau_noeth%C3%A9rien" title="Anneau noethérien">noethérien</a>. </p><p>La <a href="/wiki/Distance_(math%C3%A9matiques)" title="Distance (mathématiques)">distance</a> usuelle sur <b>Z</b> est la valeur absolue de la différence. Elle fait de <b>Z</b> un <a href="/wiki/Espace_m%C3%A9trique" title="Espace métrique">espace métrique</a> dont la <a href="/wiki/Espace_topologique" title="Espace topologique">topologie</a> est <a href="/wiki/Topologie_discr%C3%A8te" title="Topologie discrète">discrète</a>, si bien que l'espace est <a href="/wiki/Espace_complet" title="Espace complet">complet</a>. Les seules autres distances compatibles avec la structure d'anneau sont les <a href="/wiki/Nombre_p-adique" title="Nombre p-adique">distances <i>p</i>-adiques</a>, où <i>p</i> est un <a href="/wiki/Nombre_premier" title="Nombre premier">nombre premier</a>. </p><p>Le <a href="/wiki/Groupe_(math%C3%A9matiques)" title="Groupe (mathématiques)">groupe</a> additif (<b>Z</b>, +) est (<a href="/wiki/%C3%80_quelque_chose_pr%C3%A8s" title="À quelque chose près">à isomorphisme près</a>) l'unique <a href="/wiki/Groupe_monog%C3%A8ne" title="Groupe monogène">groupe monogène</a> sans <a href="/wiki/Torsion_(alg%C3%A8bre)" title="Torsion (algèbre)">torsion</a>, c'est-à-dire l'unique <a href="/wiki/Groupe_ab%C3%A9lien_libre" title="Groupe abélien libre">groupe abélien libre</a> de rang 1. C'est donc un <a href="/wiki/Groupe_infini" title="Groupe infini">groupe infini</a> <a href="/wiki/Ensemble_d%C3%A9nombrable" title="Ensemble dénombrable">dénombrable</a>. </p><p>Ce groupe est <a href="/wiki/Groupe_totalement_ordonn%C3%A9" class="mw-redirect" title="Groupe totalement ordonné">totalement ordonné</a> par la relation d'ordre usuelle. </p> <div class="mw-heading mw-heading3"><h3 id="Extensions">Extensions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=9" title="Modifier la section : Extensions" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=9" title="Modifier le code source de la section : Extensions"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'ensemble <b>Z</b> des entiers relatifs se plonge dans l'ensemble des <a href="/wiki/Nombres_d%C3%A9cimaux" class="mw-redirect" title="Nombres décimaux">nombres décimaux</a>, noté <b>D</b>, qui lui-même est une partie de l'ensemble des <a href="/wiki/Nombre_rationnel" title="Nombre rationnel">nombres rationnels</a> noté <b>Q</b>. </p><p>La notion d'entier est étendue par la définition des <a href="/wiki/Entier_alg%C3%A9brique" title="Entier algébrique">entiers algébriques</a>, qui sont aux divers <a href="/wiki/Corps_de_nombres" title="Corps de nombres">corps de nombres</a> ce que les entiers relatifs sont au corps des rationnels. Les entiers rationnels, c'est-à-dire les entiers algébriques du corps des rationnels, sont donc exactement les entiers relatifs. </p><p>Pour chacune des distances <i>p</i>-adiques, le complété de <b>Z</b> est un anneau des entiers <i>p</i>-adiques noté <b>Z</b><sub><i>p</i></sub>, dont le corps de fraction est le corps des nombres <i>p</i>-adiques, noté <b>Q</b><sub><i>p</i></sub> et qui contient <b>Q</b>. </p> <div class="mw-heading mw-heading2"><h2 id="Utilisations_courantes">Utilisations courantes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=10" title="Modifier la section : Utilisations courantes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=10" title="Modifier le code source de la section : Utilisations courantes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les nombres relatifs sont des nombres qui sont devenus relativement familiers. On les trouve : </p> <ul><li>dans les <a href="/wiki/Ascenseur" title="Ascenseur">ascenseurs</a> où par exemple -2 désignera le deuxième sous-sol ;</li> <li>sur les <a href="/wiki/Thermom%C3%A8tre" title="Thermomètre">thermomètres</a> pour indiquer les températures en dessous de <span title="32 °F ou 273,2 K" style="cursor:help">0</span> <abbr class="abbr" title="degré Celsius">°C</abbr> ;</li> <li>sur les relevés bancaires où par exemple -120 indiquera un découvert de 120 euros.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=11" title="Modifier la section : Notes et références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=11" title="Modifier le code source de la section : Notes et références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink noprint"><a href="#cite_ref-1">↑</a> </span><span class="reference-text">De cette position <i>relative à zéro</i> vient l'adjectif « relatif » appliqué à ces entiers.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-2">↑</a> </span><span class="reference-text">Selon certaines conventions différentes, en vigueur notamment dans les pays anglo-saxons, l'entier zéro n'est ni positif ni négatif (<i>cf</i> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a href="https://en.wikipedia.org/wiki/Zero" class="extiw" title="en:Zero">Zero</a>).</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink noprint"><a href="#cite_ref-3">↑</a> </span><span class="reference-text">De l'<a href="/wiki/Allemand" title="Allemand">allemand</a> <i><span class="lang-de" lang="de">Zahlen</span></i>, « nombres ».</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink noprint"><a href="#cite_ref-4">↑</a> </span><span class="reference-text"><span class="ouvrage" id="HardyWright"><span class="ouvrage" id="G._H._HardyE._M._Wright"><a href="/wiki/Godfrey_Harold_Hardy" title="Godfrey Harold Hardy">G. H. Hardy</a> et <a href="/wiki/Edward_Maitland_Wright" title="Edward Maitland Wright">E. M. Wright</a> (<abbr class="abbr" title="traduction">trad.</abbr> de l'anglais par François Sauvageot, <abbr class="abbr" title="préface">préf.</abbr> <a href="/wiki/Catherine_Goldstein" title="Catherine Goldstein">Catherine Goldstein</a>), <cite class="italique">Introduction à la théorie des nombres</cite> [« <span class="lang-en" lang="en">An Introduction to the Theory of Numbers</span> »] <small>[<a href="/wiki/R%C3%A9f%C3%A9rence:Theory_of_numbers_(HardyWright)#Édition_en_français" title="Référence:Theory of numbers (HardyWright)">détail de l’édition</a>]</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+%C3%A0+la+th%C3%A9orie+des+nombres&rft.aulast=Hardy&rft.aufirst=G.+H.&rft.au=E.+M.+Wright&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AEntier+relatif"></span></span></span>, chapitre 12.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink noprint"><a href="#cite_ref-5">↑</a> </span><span class="reference-text">Mais le <a rel="nofollow" class="external text" href="http://agreg.org/ProgAgregMath2009.pdf">programme officiel de l'agrégation de mathématiques</a>, et les <a rel="nofollow" class="external text" href="http://agreg.org/sujets.html">sujets</a> correspondants, utilisent l'appellation plus courante en France « entiers relatifs ».</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink noprint"><a href="#cite_ref-6">↑</a> </span><span class="reference-text">Cf. par exemple N. Bourbaki, <i><a href="/wiki/%C3%89l%C3%A9ments_de_math%C3%A9matique" title="Éléments de mathématique">Éléments de mathématique</a>, Algèbre</i>, chap. I, § 2, <abbr class="abbr" title="numéro">n<sup>o</sup></abbr> 5 (<abbr class="abbr" title="page">p.</abbr> 28 d'<a rel="nofollow" class="external text" href="http://portail.mathdoc.fr/archives-bourbaki/PDF/033_iecnr_040.pdf">une vieille version accessible en ligne</a>) ou <a href="/wiki/Roger_Godement" title="Roger Godement">Roger Godement</a>, <i>Cours d'algèbre</i>, § 5, <abbr class="abbr" title="numéro">n<sup>o</sup></abbr> 8.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink noprint"><a href="#cite_ref-7">↑</a> </span><span class="reference-text">Paradoxe classique : si -1 < 1 alors les inverses de ces deux nombres seraient rangés dans l'ordre inverse : l'inverse de -1 est -1 et l'inverse de 1 est 1 donc -1 > 1. paradoxe qui provient de la phrase incomplète "les inverses de ces deux nombres seraient rangés dans l'ordre inverse", il faudrait préciser "les inverses de deux nombres <b>de même signe</b> sont rangés dans l'ordre inverse". Voir l'article <a href="/wiki/Fonction_inverse" title="Fonction inverse">fonction inverse</a> pour plus d'informations.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink noprint"><a href="#cite_ref-8">↑</a> </span><span class="reference-text"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a rel="nofollow" class="external text" href="http://jeff560.tripod.com/nth.html">Earliest Uses of Symbols of Number Theory</a>.</span> </li> </ol></div> </div> <div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Entier_relatif&veaction=edit&section=12" title="Modifier la section : Voir aussi" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Entier_relatif&action=edit&section=12" title="Modifier le code source de la section : Voir aussi"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r194021218">.mw-parser-output .autres-projets>.titre{text-align:center;margin:0.2em 0}.mw-parser-output .autres-projets>ul{margin:0;padding:0}.mw-parser-output .autres-projets>ul>li{list-style:none;margin:0.2em 0;text-indent:0;padding-left:24px;min-height:20px;text-align:left;display:block}.mw-parser-output .autres-projets>ul>li>a{font-style:italic}@media(max-width:720px){.mw-parser-output .autres-projets{float:none}}</style><div class="autres-projets boite-grise boite-a-droite noprint js-interprojets"> <p class="titre">Sur les autres projets Wikimedia :</p> <ul class="noarchive plainlinks"> <li class="wikiversity"><a href="https://fr.wikiversity.org/wiki/Nombre_entier_relatif" class="extiw" title="v:Nombre entier relatif">Entier relatif</a>, <span class="nowrap">sur <span class="project">Wikiversity</span></span></li> </ul> </div> <p><a href="/wiki/Entier_(informatique)" title="Entier (informatique)">Entier (informatique)</a> </p> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint collapsed" style=""> <tbody><tr><th class="navbox-title" colspan="3" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_Notion_de_nombre" title="Modèle:Palette Notion de nombre"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_Notion_de_nombre&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%">Notion de <a href="/wiki/Nombre" title="Nombre">nombre</a></div></th> </tr> <tr> <th class="navbox-group" style="">Ensembles usuels</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Entier_naturel" title="Entier naturel">Entier naturel</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40eac26c488d3257e3fbe63619729673145d228c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.187ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {N} }"></span>)</li> <li><a class="mw-selflink selflink">Entier relatif</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0c672518c0350ca035befd41c26633a2d399431" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.096ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {Z} }"></span>)</li> <li><a href="/wiki/Nombre_d%C3%A9cimal" title="Nombre décimal">Nombre décimal</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {D} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {D} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3f303c0b908a47cc0dfb5e7a7293a94a22dd0bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.187ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {D} }"></span>)</li> <li><a href="/wiki/Nombre_rationnel" title="Nombre rationnel">Nombre rationnel</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/feaa5ab94a056a5a25944ddf0c52c92a404715ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.279ex; height:1.843ex;" alt="{\displaystyle \scriptstyle \mathbb {Q} }"></span>)</li> <li><a href="/wiki/Nombre_r%C3%A9el" title="Nombre réel">Nombre réel</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac7df6838b44979c6531f6a0306206fbdb0477ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.187ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {R} }"></span>)</li> <li><a href="/wiki/Nombre_complexe" title="Nombre complexe">Nombre complexe</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe3a54bb4e56c039e18c3af24ba70ab377f7a07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.187ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {C} }"></span>)</li></ul> </div></td> <td class="navbox-image" rowspan="5" style="vertical-align:middle;padding-left:7px"><span typeof="mw:File"><a href="/wiki/Fichier:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description" title="Mathématiques"><img alt="Mathématiques" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/70px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="70" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/105px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/140px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></td> </tr> <tr> <th class="navbox-group" style="">Extensions</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Quaternion" title="Quaternion">Quaternion</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {H} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">H</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {H} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d00daea5df233d805f1ec5d5ae84845bac2ad06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.279ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {H} }"></span>)</li> <li><a href="/wiki/Octonion" title="Octonion">Octonion</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {O} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">O</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {O} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c5cf3960cf7ba384648447c15581d5d4589a6d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.279ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {O} }"></span>)</li> <li><a href="/wiki/S%C3%A9d%C3%A9nion" title="Sédénion">Sédénion</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">S</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {S} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ef48a593f4503abeab608e8781ba478b7d1b304" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.914ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {S} }"></span>)</li> <li><a href="/wiki/Nombre_complexe_d%C3%A9ploy%C3%A9" title="Nombre complexe déployé">Nombre complexe déployé</a></li> <li><a href="/wiki/Tessarine" title="Tessarine">Tessarine</a></li> <li><a href="/wiki/Nombre_bicomplexe" title="Nombre bicomplexe">Nombre bicomplexe</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {C} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {C} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba9ab8af8ff8f4437f3c72de4e78738374ee4954" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.018ex; height:1.843ex;" alt="{\displaystyle \scriptstyle \mathbb {C} _{2}}"></span>)</li> <li>Nombre multicomplexe (<a href="/wiki/Nombre_multicomplexe_(Segre)" title="Nombre multicomplexe (Segre)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {C} _{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {C} _{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee4170ef11ece45d8b66656c919e34eefdb51e42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.151ex; height:1.843ex;" alt="{\displaystyle \scriptstyle \mathbb {C} _{n}}"></span></a></li> <li><a href="/wiki/Nombre_multicomplexe_(Fleury)" title="Nombre multicomplexe (Fleury)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\mathcal {M}}\mathbb {C} _{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\mathcal {M}}\mathbb {C} _{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7be2600f9a2a7a3fdbdb7b08d21dec751dfde32e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.125ex; height:1.843ex;" alt="{\displaystyle \scriptstyle {\mathcal {M}}\mathbb {C} _{n}}"></span></a>)</li> <li><a href="/wiki/Biquaternion" title="Biquaternion">Biquaternion</a></li> <li><a href="/wiki/Coquaternion" title="Coquaternion">Coquaternion</a></li> <li><a href="/wiki/Quaternion_hyperbolique" title="Quaternion hyperbolique">Quaternion hyperbolique</a></li> <li><a href="/wiki/Octonion_d%C3%A9ploy%C3%A9" title="Octonion déployé">Octonion déployé</a></li> <li><a href="/wiki/Nombre_hypercomplexe" title="Nombre hypercomplexe">Nombre hypercomplexe</a></li> <li><a href="/wiki/Nombre_p-adique" title="Nombre p-adique">Nombre p-adique</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {Q} _{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {Q} _{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/425658dc852cec8a2d4b6f7d513e60977710d7f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.114ex; height:2.176ex;" alt="{\displaystyle \scriptstyle \mathbb {Q} _{p}}"></span>)</li> <li><a href="/wiki/Nombre_hyperr%C3%A9el" title="Nombre hyperréel">Nombre hyperréel</a></li> <li><a href="/wiki/Nombre_superr%C3%A9el" title="Nombre superréel">Nombre superréel</a></li> <li><a href="/wiki/Nombre_dual" title="Nombre dual">Nombre dual</a></li> <li><a href="/wiki/Droite_r%C3%A9elle_achev%C3%A9e" title="Droite réelle achevée">Droite réelle achevée</a></li> <li><a href="/wiki/Nombre_cardinal" title="Nombre cardinal">Nombre cardinal</a></li> <li><a href="/wiki/Nombre_ordinal" title="Nombre ordinal">Nombre ordinal</a></li> <li><a href="/wiki/Nombre_surr%C3%A9el" title="Nombre surréel">Nombre surréel</a></li> <li><a href="/wiki/Nombre_pseudo-r%C3%A9el" title="Nombre pseudo-réel">Nombre pseudo-réel</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Propriétés particulières</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Parit%C3%A9_(arithm%C3%A9tique)" title="Parité (arithmétique)">Parité</a></li> <li><a href="/wiki/Nombre_premier" title="Nombre premier">Nombre premier</a></li> <li><a href="/wiki/Nombre_compos%C3%A9" title="Nombre composé">Nombre composé</a></li> <li><a href="/wiki/Nombre_figur%C3%A9" title="Nombre figuré">Nombre figuré</a></li> <li><a href="/wiki/Nombre_parfait" title="Nombre parfait">Nombre parfait</a></li> <li><a href="/wiki/Nombre_positif" title="Nombre positif">Nombre positif</a></li> <li><a href="/wiki/Nombre_n%C3%A9gatif" title="Nombre négatif">Nombre négatif</a></li> <li><a href="/wiki/Fraction_dyadique" title="Fraction dyadique">Fraction dyadique</a></li> <li><span typeof="mw:File"><span title="Bon article"><img alt="Bon article" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/14px-Bon_article.svg.png" decoding="async" width="14" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/21px-Bon_article.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/28px-Bon_article.svg.png 2x" data-file-width="20" data-file-height="20" /></span></span> <a href="/wiki/Nombre_irrationnel" title="Nombre irrationnel">Nombre irrationnel</a></li> <li><a href="/wiki/Nombre_alg%C3%A9brique" title="Nombre algébrique">Nombre algébrique</a></li> <li><a href="/wiki/Nombre_transcendant" title="Nombre transcendant">Nombre transcendant</a></li> <li><a href="/wiki/Nombre_imaginaire_pur" title="Nombre imaginaire pur">Nombre imaginaire pur</a></li> <li><a href="/wiki/Nombre_de_Liouville" title="Nombre de Liouville">Nombre de Liouville</a></li> <li><a href="/wiki/Alg%C3%A8bre_des_p%C3%A9riodes" title="Algèbre des périodes">Période</a></li> <li><a href="/wiki/Nombre_normal" title="Nombre normal">Nombre normal</a></li> <li><a href="/wiki/Nombre_univers" title="Nombre univers">Nombre univers</a></li> <li><a href="/wiki/Nombre_constructible" title="Nombre constructible">Nombre constructible</a></li> <li><a href="/wiki/Nombre_r%C3%A9el_calculable" title="Nombre réel calculable">Nombre réel calculable</a></li> <li><a href="/wiki/Nombre_transfini" title="Nombre transfini">Nombre transfini</a></li> <li><a href="/wiki/Infiniment_petit" title="Infiniment petit">Infiniment petit</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Exemples</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Pi" title="Pi">Pi</a> (<span class="texhtml">π</span>)</li> <li><span typeof="mw:File"><span title="Bon article"><img alt="Bon article" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/14px-Bon_article.svg.png" decoding="async" width="14" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/21px-Bon_article.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/28px-Bon_article.svg.png 2x" data-file-width="20" data-file-height="20" /></span></span> <a href="/wiki/Racine_carr%C3%A9e_de_deux" title="Racine carrée de deux">Racine carrée de deux</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b6ac02637a190523aa10dde1b52ae41964dfff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.191ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {\sqrt {2}}}"></span>)</li> <li><span typeof="mw:File"><span title="Bon article"><img alt="Bon article" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/14px-Bon_article.svg.png" decoding="async" width="14" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/21px-Bon_article.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Bon_article.svg/28px-Bon_article.svg.png 2x" data-file-width="20" data-file-height="20" /></span></span> <a href="/wiki/Nombre_d%27or" title="Nombre d'or">Nombre d’or</a> (φ)</li> <li><a href="/wiki/Z%C3%A9ro" title="Zéro">Zéro</a> (0)</li> <li><a href="/wiki/Unit%C3%A9_imaginaire" title="Unité imaginaire">Unité imaginaire</a> (<span class="texhtml">i</span>)</li> <li><a href="/wiki/E_(nombre)" title="E (nombre)">Constante de Neper</a> (<span class="texhtml">e</span>)</li> <li><a href="/wiki/Aleph-z%C3%A9ro" title="Aleph-zéro">Aleph-zéro</a> (ℵ<sub>0</sub>)</li> <li><a href="/wiki/Table_de_constantes_math%C3%A9matiques" title="Table de constantes mathématiques">Table de constantes mathématiques</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Articles liés</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Chiffre" title="Chiffre">Chiffre</a></li> <li><a href="/wiki/Num%C3%A9ration" title="Numération">Numération</a></li> <li><a href="/wiki/Fraction_(math%C3%A9matiques)" title="Fraction (mathématiques)">Fraction</a></li> <li><a href="/wiki/Op%C3%A9ration_(math%C3%A9matiques)" title="Opération (mathématiques)">Opération</a></li> <li><a href="/wiki/Calcul_(math%C3%A9matiques)" title="Calcul (mathématiques)">Calcul</a></li> <li><a href="/wiki/Alg%C3%A8bre" title="Algèbre">Algèbre</a></li> <li><a href="/wiki/Arithm%C3%A9tique" title="Arithmétique">Arithmétique</a></li> <li><a href="/wiki/Suite_d%27entiers" title="Suite d'entiers">Suite d'entiers</a></li> <li><a href="/wiki/Infini" title="Infini">Infini</a> (<span class="texhtml">∞</span>)</li> <li><a href="/wiki/Chiffre_significatif" title="Chiffre significatif">Chiffre significatif</a></li></ul> </div></td> </tr> </tbody></table> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer skin-invert-image" typeof="mw:File"><a href="/wiki/Portail:Arithm%C3%A9tique_et_th%C3%A9orie_des_nombres" title="Arithmétique et théorie des nombres"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pascal%27s_triangle_5.svg/34px-Pascal%27s_triangle_5.svg.png" decoding="async" width="34" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pascal%27s_triangle_5.svg/50px-Pascal%27s_triangle_5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pascal%27s_triangle_5.svg/67px-Pascal%27s_triangle_5.svg.png 2x" data-file-width="540" data-file-height="389" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Arithm%C3%A9tique_et_th%C3%A9orie_des_nombres" title="Portail:Arithmétique et théorie des nombres">Arithmétique et théorie des nombres</a></span> </span></li> </ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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