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class="vector-toc-link" href="#En_analyse_mathématique"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>En analyse mathématique</span> </div> </a> <ul id="toc-En_analyse_mathématique-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Infiniment_grands" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Infiniment_grands"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Infiniment grands</span> </div> </a> <ul id="toc-Infiniment_grands-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Médias" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Médias"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Médias</span> </div> </a> <ul id="toc-Médias-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Littérature" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Littérature"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Littérature</span> </div> </a> <ul id="toc-Littérature-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-Annexes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Annexes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Annexes</span> </div> </a> <button aria-controls="toc-Annexes-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 Annexes</span> </button> <ul id="toc-Annexes-sublist" class="vector-toc-list"> <li id="toc-Articles_connexes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Articles_connexes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Articles connexes</span> </div> </a> <ul id="toc-Articles_connexes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lien_externe" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lien_externe"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Lien externe</span> </div> </a> <ul id="toc-Lien_externe-sublist" class="vector-toc-list"> </ul> </li> </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">Infiniment petit</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 45 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-45" 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">45 langues</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AA%D9%86%D8%A7%D9%87%D9%8A_%D8%A7%D9%84%D8%B5%D8%BA%D8%B1_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="متناهي الصغر (رياضيات) – arabe" lang="ar" hreflang="ar" data-title="متناهي الصغر (رياضيات)" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B5%D8%BA%D9%8A%D9%88%D8%B1%D8%A7%D9%86%D9%8A" title="صغيوراني – arabe marocain" lang="ary" hreflang="ary" data-title="صغيوراني" data-language-autonym="الدارجة" data-language-local-name="arabe marocain" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D1%8F%D1%81%D0%BA%D0%BE%D0%BD%D1%86%D0%B0_%D0%BC%D0%B0%D0%BB%D0%B0%D1%8F_%D0%B2%D0%B5%D0%BB%D1%96%D1%87%D1%8B%D0%BD%D1%8F" title="Бясконца малая велічыня – biélorusse" lang="be" hreflang="be" data-title="Бясконца малая велічыня" data-language-autonym="Беларуская" data-language-local-name="biélorusse" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B6%E0%A7%82%E0%A6%A8%E0%A7%8D%E0%A6%AF%E0%A6%B8%E0%A6%A8%E0%A7%8D%E0%A6%A8%E0%A6%BF%E0%A6%95%E0%A6%B0%E0%A7%8D%E0%A6%B7%E0%A7%80" title="শূন্যসন্নিকর্ষী – bengali" lang="bn" hreflang="bn" data-title="শূন্যসন্নিকর্ষী" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/M%C3%A8todes_infinitesimals" title="Mètodes infinitesimals – catalan" lang="ca" hreflang="ca" data-title="Mètodes infinitesimals" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Infinitezim%C3%A1ln%C3%AD_hodnota" title="Infinitezimální hodnota – tchèque" lang="cs" hreflang="cs" data-title="Infinitezimální hodnota" 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%92%C4%95%C3%A7%D1%81%C4%95%D1%80_%D0%BF%C4%95%D1%87%C4%95%D0%BA_%D1%82%D0%B0%D1%82%D0%B0_%D0%B2%C4%95%C3%A7%D1%81%C4%95%D1%80_%D0%BF%D1%8B%D1%81%C4%83%D0%BA" title="Вĕçсĕр пĕчĕк тата вĕçсĕр пысăк – tchouvache" lang="cv" hreflang="cv" data-title="Вĕçсĕр пĕчĕк тата вĕçсĕр пысăк" data-language-autonym="Чӑвашла" data-language-local-name="tchouvache" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Infinitesimal" title="Infinitesimal – danois" lang="da" hreflang="da" data-title="Infinitesimal" 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/Infinitesimalzahl" title="Infinitesimalzahl – allemand" lang="de" hreflang="de" data-title="Infinitesimalzahl" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Infinitesimal" title="Infinitesimal – anglais" lang="en" hreflang="en" data-title="Infinitesimal" 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/Senfinecono" title="Senfinecono – espéranto" lang="eo" hreflang="eo" data-title="Senfinecono" 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/Infinitesimal" title="Infinitesimal – espagnol" lang="es" hreflang="es" data-title="Infinitesimal" 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/Infinitesimaalarv" title="Infinitesimaalarv – estonien" lang="et" hreflang="et" data-title="Infinitesimaalarv" 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/Infinitesimo" title="Infinitesimo – basque" lang="eu" hreflang="eu" data-title="Infinitesimo" 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%A8%DB%8C%E2%80%8C%D9%86%D9%87%D8%A7%DB%8C%D8%AA%E2%80%8C%DA%A9%D9%88%DA%86%DA%A9" title="بی‌نهایت‌کوچک – persan" lang="fa" hreflang="fa" data-title="بی‌نهایت‌کوچک" 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/Infinitesimaali" title="Infinitesimaali – finnois" lang="fi" hreflang="fi" data-title="Infinitesimaali" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Infinitesimal" title="Infinitesimal – galicien" lang="gl" hreflang="gl" data-title="Infinitesimal" data-language-autonym="Galego" data-language-local-name="galicien" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%99%D7%A0%D7%A4%D7%99%D7%A0%D7%99%D7%98%D7%A1%D7%99%D7%9E%D7%9C" title="אינפיניטסימל – hébreu" lang="he" hreflang="he" data-title="אינפיניטסימל" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B6%D5%BE%D5%A5%D6%80%D5%BB_%D6%83%D5%B8%D6%84%D6%80" title="Անվերջ փոքր – arménien" lang="hy" hreflang="hy" data-title="Անվերջ փոքր" data-language-autonym="Հայերեն" data-language-local-name="arménien" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Infinitesimal" title="Infinitesimal – indonésien" lang="id" hreflang="id" data-title="Infinitesimal" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Infinitesimo" title="Infinitesimo – italien" lang="it" hreflang="it" data-title="Infinitesimo" 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/%E7%84%A1%E9%99%90%E5%B0%8F" title="無限小 – japonais" lang="ja" hreflang="ja" data-title="無限小" 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-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D2%9B%D1%8B%D1%80%D1%81%D1%8B%D0%B7_%D0%B0%D0%B7%D0%B4%D0%B0%D1%80_%D2%9B%D0%B8%D1%81%D0%B0%D0%B1%D1%8B" title="Ақырсыз аздар қисабы – kazakh" lang="kk" hreflang="kk" data-title="Ақырсыз аздар қисабы" 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/%EB%AC%B4%ED%95%9C%EC%86%8C" title="무한소 – coréen" lang="ko" hreflang="ko" data-title="무한소" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%98%D0%BD%D1%84%D0%B8%D0%BD%D0%B8%D1%82%D0%B5%D0%B7%D0%B8%D0%BC%D0%B0%D0%BB%D0%B0" title="Инфинитезимала – macédonien" lang="mk" hreflang="mk" data-title="Инфинитезимала" 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%85%E0%B4%A8%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%B8%E0%B5%82%E0%B4%95%E0%B5%8D%E0%B4%B7%E0%B5%8D%E0%B4%AE%E0%B4%82" title="അനന്തസൂക്ഷ്മം – malayalam" lang="ml" hreflang="ml" data-title="അനന്തസൂക്ഷ്മം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%90%E1%80%99%E1%80%BD%E1%80%90%E1%80%BA%E1%80%85%E1%80%AD%E1%80%90%E1%80%BA%E1%80%A1%E1%80%95%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8" title="တမွတ်စိတ်အပိုင်း – birman" lang="my" hreflang="my" data-title="တမွတ်စိတ်အပိုင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birman" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Infinitesimaal" title="Infinitesimaal – néerlandais" lang="nl" hreflang="nl" data-title="Infinitesimaal" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Niesko%C5%84czenie_ma%C5%82e" title="Nieskończenie małe – polonais" lang="pl" hreflang="pl" data-title="Nieskończenie małe" data-language-autonym="Polski" data-language-local-name="polonais" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Infinitesimal" title="Infinitesimal – portugais" lang="pt" hreflang="pt" data-title="Infinitesimal" 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/Infinitezimal" title="Infinitezimal – roumain" lang="ro" hreflang="ro" data-title="Infinitezimal" data-language-autonym="Română" data-language-local-name="roumain" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE_%D0%BC%D0%B0%D0%BB%D0%B0%D1%8F_%D0%B8_%D0%B1%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE_%D0%B1%D0%BE%D0%BB%D1%8C%D1%88%D0%B0%D1%8F" title="Бесконечно малая и бесконечно большая – russe" lang="ru" hreflang="ru" data-title="Бесконечно малая и бесконечно большая" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Infinitesimal" title="Infinitesimal – Simple English" lang="en-simple" hreflang="en-simple" data-title="Infinitesimal" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Infinitezimala" title="Infinitezimala – slovène" lang="sl" hreflang="sl" data-title="Infinitezimala" data-language-autonym="Slovenščina" data-language-local-name="slovène" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Infinitezimale" title="Infinitezimale – albanais" lang="sq" hreflang="sq" data-title="Infinitezimale" 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%98%D0%BD%D1%84%D0%B8%D0%BD%D0%B8%D1%82%D0%B5%D0%B7%D0%B8%D0%BC%D0%B0%D0%BB%D0%B0%D0%BD" title="Инфинитезималан – serbe" lang="sr" hreflang="sr" data-title="Инфинитезималан" 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/Infinitesimal" title="Infinitesimal – suédois" lang="sv" hreflang="sv" data-title="Infinitesimal" 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/Kiduchu_(hisabati)" title="Kiduchu (hisabati) – swahili" lang="sw" hreflang="sw" data-title="Kiduchu (hisabati)" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%93%E0%B8%B4%E0%B8%81%E0%B8%99%E0%B8%B1%E0%B8%99%E0%B8%95%E0%B9%8C" title="กณิกนันต์ – thaï" lang="th" hreflang="th" data-title="กณิกนันต์" data-language-autonym="ไทย" data-language-local-name="thaï" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sonsuz_k%C3%BC%C3%A7%C3%BCk" title="Sonsuz küçük – turc" lang="tr" hreflang="tr" data-title="Sonsuz küçük" 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%9D%D0%B5%D1%81%D0%BA%D1%96%D0%BD%D1%87%D0%B5%D0%BD%D0%BD%D0%BE_%D0%BC%D0%B0%D0%BB%D0%B0_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D0%B0" title="Нескінченно мала величина – ukrainien" lang="uk" hreflang="uk" data-title="Нескінченно мала величина" 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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/Infiniment" class="mw-disambig" title="Infiniment">Infiniment</a>. </p> </div></div> <div class="bandeau-container metadata bandeau-article bandeau-niveau-ebauche"><div class="bandeau-cell bandeau-icone" style="display:table-cell;padding-right:0.5em"><span class="noviewer" typeof="mw:File"><a href="/wiki/Fichier:Racine_carr%C3%A9e_bleue.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Racine_carr%C3%A9e_bleue.svg/35px-Racine_carr%C3%A9e_bleue.svg.png" decoding="async" width="35" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Racine_carr%C3%A9e_bleue.svg/53px-Racine_carr%C3%A9e_bleue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Racine_carr%C3%A9e_bleue.svg/70px-Racine_carr%C3%A9e_bleue.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p><strong class="bandeau-titre">Cet article est une <a href="/wiki/Aide:%C3%89bauche" title="Aide:Ébauche">ébauche</a> concernant les <a href="/wiki/Math%C3%A9matiques" title="Mathématiques">mathématiques</a>.</strong> </p><p>Vous pouvez partager vos connaissances en l’améliorant (<b><a href="/wiki/Aide:Comment_modifier_une_page" title="Aide:Comment modifier une page">comment ?</a></b>) selon les recommandations des <a href="/wiki/Projet:Accueil" title="Projet:Accueil">projets correspondants</a>. </p> </div></div> <p>Les <b>infinitésimaux</b> (ou <b>infiniment petits</b>) ont été utilisés pour exprimer l'idée d'objets si petits qu'il n'y a pas moyen de les voir ou de les mesurer. Le mot <span class="citation">« infinitésimal »</span> vient de <i>infinitesimus</i> (latin du <abbr class="abbr" title="17ᵉ siècle"><span class="romain">XVII</span><sup style="font-size:72%">e</sup></abbr> siècle), ce qui signifiait à l'origine l'élément <span class="citation">« infini-ème »</span> dans une série. Selon la <a href="/wiki/Notation_de_Leibniz" title="Notation de Leibniz">notation de Leibniz</a>, si <i>x</i> est une quantité, d<i>x</i> et Δ<i>x</i> peuvent représenter une quantité infinitésimale de <i>x</i>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historique">Historique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infiniment_petit&veaction=edit&section=1" title="Modifier la section : Historique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infiniment_petit&action=edit&section=1" title="Modifier le code source de la section : Historique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dans le langage courant, un objet <b>infiniment petit</b> est un objet qui est plus petit que toute mesure possible, donc non pas d'une taille zéro, mais si petit qu'il ne peut être distingué de zéro par aucun moyen disponible. Par conséquent, lorsqu'il est utilisé en tant qu'adjectif, «infinitésimal» dans le <a href="/wiki/Langue_vernaculaire" title="Langue vernaculaire">langage vernaculaire</a> signifie <span class="citation">« extrêmement faible »</span>. </p><p><a href="/wiki/Archim%C3%A8de" title="Archimède">Archimède</a> exploita les infinitésimaux dans <i><a href="/wiki/Trait%C3%A9_de_la_M%C3%A9thode" title="Traité de la Méthode">La Méthode</a></i> pour trouver des aires des régions et des volumes de solides. Les auteurs classiques avaient tendance à chercher à remplacer les arguments infinitésimaux par des arguments utilisant la <a href="/wiki/M%C3%A9thode_d%27exhaustion" title="Méthode d'exhaustion">méthode d'exhaustion</a>, qu'ils jugeaient plus fiable. Le <abbr class="abbr" title="15ᵉ siècle"><span class="romain">XV</span><sup style="font-size:72%">e</sup></abbr> siècle a vu le travail pionnier de <a href="/wiki/Nicolas_de_Cues" title="Nicolas de Cues">Nicolas de Cues</a>, développé au <abbr class="abbr" title="17ᵉ siècle"><span class="romain">XVII</span><sup style="font-size:72%">e</sup></abbr> siècle par <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a>, en particulier le calcul de l'aire d'un cercle en représentant celui-ci comme un polygone d'un nombre infini de côtés. <a href="/wiki/Simon_Stevin" title="Simon Stevin">Simon Stevin</a> élabora un continu de décimaux au <abbr class="abbr" title="16ᵉ siècle"><span class="romain">XVI</span><sup style="font-size:72%">e</sup></abbr> siècle. La <a href="/wiki/M%C3%A9thode_des_indivisibles" title="Méthode des indivisibles">méthode des indivisibles</a> de <a href="/wiki/Bonaventura_Cavalieri" title="Bonaventura Cavalieri">Bonaventura Cavalieri</a> conduit à une extension des résultats des auteurs classiques. La méthode des indivisibles traitait des figures géométriques comme étant composés d'entités de <a href="/wiki/Codimension" title="Codimension">codimension</a> 1. Les infinitésimaux de <a href="/wiki/John_Wallis" title="John Wallis">John Wallis</a> diffèrent des indivisibles en ce sens que des figures géométriques se décomposeraient en des parties infiniment minces de la même dimension que la figure, préparant le terrain pour des méthodes générales du <a href="/wiki/Calcul_int%C3%A9gral" class="mw-redirect" title="Calcul intégral">calcul intégral</a>. Il exploita un infinitésimal noté <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 {\frac {1}{\infty }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi mathvariant="normal">∞</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\infty }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd40fade822de7f56646c7006e7f12744b4a275d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.16ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{\infty }}}"></span> dans les calculs de superficie. </p><p><a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a>, inspiré par <a href="/wiki/Diophante_d%27Alexandrie" title="Diophante d'Alexandrie">Diophante</a>, développa le concept d'<a href="/wiki/Ad%C3%A9galit%C3%A9" title="Adégalité">adégalité</a>, c'est-à-dire égalité « adéquate » ou égalité approximative (avec une erreur infime), qui a fini par jouer un rôle clé dans une mise en œuvre mathématique moderne des définitions infinitésimales de la <a href="/wiki/D%C3%A9riv%C3%A9e" title="Dérivée">dérivée</a> et l'<a href="/wiki/Int%C3%A9gration_(math%C3%A9matiques)" title="Intégration (mathématiques)">intégrale</a>. L'utilisation des infinitésimaux chez <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a> s'appuya sur un principe heuristique appelé la <a href="/wiki/Principe_de_continuit%C3%A9" title="Principe de continuité">loi de continuité</a> : ce qui réussit pour les nombres finis réussit aussi pour les nombres infinis, et <i>vice versa</i>. Le <abbr class="abbr" title="18ᵉ siècle"><span class="romain">XVIII</span><sup style="font-size:72%">e</sup></abbr> siècle a vu l'utilisation systématique des infiniment petits par les plus grands tels que <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> et <a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Joseph-Louis Lagrange</a>. <a href="/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy">Augustin-Louis Cauchy</a> exploita les infinitésimaux dans sa définition de la <a href="/wiki/Continuit%C3%A9_(math%C3%A9matiques)" title="Continuité (mathématiques)">continuité</a> et dans une forme préliminaire d'une <a href="/wiki/Distribution_de_Dirac" title="Distribution de Dirac">fonction delta de Dirac</a>. Lorsque <a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a> et <a href="/wiki/Richard_Dedekind" title="Richard Dedekind">Dedekind</a> développaient des versions plus abstraites du continu de Stevin, <a href="/wiki/Paul_David_Gustave_du_Bois-Reymond" title="Paul David Gustave du Bois-Reymond">Paul du Bois-Reymond</a> a écrit une série d'articles sur des continus enrichis d'infinitésimaux sur la base des taux de croissance des fonctions. L'œuvre de du Bois-Reymond a inspiré à la fois <a href="/wiki/%C3%89mile_Borel" title="Émile Borel">Émile Borel</a> et <a href="/wiki/Thoralf_Skolem" title="Thoralf Skolem">Thoralf Skolem</a>. Skolem développa les premiers <a href="/wiki/Mod%C3%A8le_non_standard" title="Modèle non standard">modèles non standard</a> de l'arithmétique en 1934. Une mise en œuvre mathématique à la fois de la loi de continuité et des infinitésimaux a été réalisée par <a href="/wiki/Abraham_Robinson" title="Abraham Robinson">Abraham Robinson</a> en 1961, qui a développé l'<a href="/wiki/Analyse_non_standard" title="Analyse non standard">analyse non standard</a> basée sur des travaux antérieurs de <a href="/wiki/Edwin_Hewitt" title="Edwin Hewitt">Edwin Hewitt</a> en 1948 et <a href="/w/index.php?title=Jerzy_%C5%81o%C5%9B&action=edit&redlink=1" class="new" title="Jerzy Łoś (page inexistante)">Jerzy Łoś</a> <a href="https://de.wikipedia.org/wiki/Jerzy_%C5%81o%C5%9B" class="extiw" title="de:Jerzy Łoś"><span class="indicateur-langue" title="Article en allemand : « Jerzy Łoś »">(de)</span></a> en 1955. Les <a href="/wiki/Nombre_hyperr%C3%A9el" title="Nombre hyperréel">hyperréels</a> constituent un continu enrichi d'infinitésimaux, tandis que le <a href="/w/index.php?title=Principe_du_transfert&action=edit&redlink=1" class="new" title="Principe du transfert (page inexistante)">principe du transfert</a> <a href="https://en.wikipedia.org/wiki/Transfer_principle" class="extiw" title="en:Transfer principle"><span class="indicateur-langue" title="Article en anglais : « Transfer principle »">(en)</span></a> met en œuvre la loi de continuité de Leibniz. </p> <div class="mw-heading mw-heading2"><h2 id="En_analyse_mathématique"><span id="En_analyse_math.C3.A9matique"></span>En analyse mathématique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infiniment_petit&veaction=edit&section=2" title="Modifier la section : En analyse mathématique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infiniment_petit&action=edit&section=2" title="Modifier le code source de la section : En analyse mathématique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <a href="/wiki/Math%C3%A9matiques" title="Mathématiques">mathématiques</a>, le terme infiniment petit peut s'appliquer : </p> <ul><li>à une quantité <a href="/wiki/Fonction_n%C3%A9gligeable" class="mw-redirect" title="Fonction négligeable">négligeable</a> dans le cadre de méthodes d'étude du comportement d'une fonction au voisinage d'un point (ou de l'infini), en regard du comportement d'une autre fonction, souvent choisie sur une échelle de référence.</li> <li>à une notion historique de nombre infinitésimal, abandonnée par les élèves de <a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a>, qui donna un fondement rigoureux à la notion de <a href="/wiki/Limite_(math%C3%A9matiques)" title="Limite (mathématiques)">limite</a>. Cette notion avait déjà été entrevue mais jamais explicitée<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>, en particulier parce que les représentations et la définition des <a href="/wiki/Nombre_r%C3%A9el" title="Nombre réel">nombres réels</a> avaient demandé une longue maturation<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>.</li> <li>à un <a href="/wiki/Nombre_hyperr%C3%A9el" title="Nombre hyperréel">nombre hyperréel</a> plus petit en <a href="/wiki/Valeur_absolue" title="Valeur absolue">valeur absolue</a> que tout inverse d’un entier, dans le cadre de l'<a href="/wiki/Analyse_non_standard" title="Analyse non standard">analyse non standard</a> de Robinson qui formalisa les infinitésimaux de <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a> ;</li> <li>de façon plus classique, en <a href="/wiki/Analyse_r%C3%A9elle" title="Analyse réelle">analyse réelle</a>, dans l'expression <span class="citation">« infiniment petits équivalents »</span> : deux fonctions <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> et <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 g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span> sont des infiniment petits équivalents au <a href="/wiki/Voisinage_(math%C3%A9matiques)" title="Voisinage (mathématiques)">voisinage</a> de a si, <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 f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.418ex; height:2.843ex;" alt="{\displaystyle f(x)}"></span> et <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 g(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6ca91363022bd5e4dcb17e5ef29f78b8ef00b59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.255ex; height:2.843ex;" alt="{\displaystyle g(x)}"></span> tendant tous deux vers zéro quand x tend vers a, le rapport <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 f(x)/g(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)/g(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b315e81de2a653c2f6c2a03f980c0e5c3ae267b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.835ex; height:2.843ex;" alt="{\displaystyle f(x)/g(x)}"></span> tend vers 1 : <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 \lim _{x\to a}{\frac {f(x)}{g(x)}}=1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi>a</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to a}{\frac {f(x)}{g(x)}}=1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cd021b7d0838a5da1b8b7380d3d42a69e0c14e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:14.002ex; height:6.509ex;" alt="{\displaystyle \lim _{x\to a}{\frac {f(x)}{g(x)}}=1.}"></span></li></ul> <p>Ainsi, la <a href="/wiki/Longueur_d%27un_arc" title="Longueur d'un arc">longueur d'un arc</a> de cercle et celle de sa corde, en tant que fonctions de l'angle au centre associé, sont des infiniment petits équivalents au voisinage de l'angle nul. </p> <div class="mw-heading mw-heading2"><h2 id="Infiniment_grands">Infiniment grands</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infiniment_petit&veaction=edit&section=3" title="Modifier la section : Infiniment grands" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infiniment_petit&action=edit&section=3" title="Modifier le code source de la section : Infiniment grands"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De même, deux fonctions <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> et <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 g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span> sont des infiniment grands équivalents au voisinage de a si, <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 f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.418ex; height:2.843ex;" alt="{\displaystyle f(x)}"></span> et <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 g(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6ca91363022bd5e4dcb17e5ef29f78b8ef00b59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.255ex; height:2.843ex;" alt="{\displaystyle g(x)}"></span> tendant tous deux vers l'infini quand x tend vers a, le rapport <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 f(x)/g(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)/g(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b315e81de2a653c2f6c2a03f980c0e5c3ae267b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.835ex; height:2.843ex;" alt="{\displaystyle f(x)/g(x)}"></span> tend vers 1. En analyse non standard, les infiniment grands sont des hyperréels qui sont les inverses des infiniment petits. </p> <div class="mw-heading mw-heading2"><h2 id="Médias"><span id="M.C3.A9dias"></span>Médias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infiniment_petit&veaction=edit&section=4" title="Modifier la section : Médias" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infiniment_petit&action=edit&section=4" title="Modifier le code source de la section : Médias"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les expressions <span class="citation">« infiniment petit »</span> et <span class="citation">« infiniment grand »</span> sont très notoires et presque jamais utilisées dans leur sens premier, mais pour parler de sujets tels que les galaxies, les quarks, et les nanotechnologies. </p> <div class="mw-heading mw-heading2"><h2 id="Littérature"><span id="Litt.C3.A9rature"></span>Littérature</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infiniment_petit&veaction=edit&section=5" title="Modifier la section : Littérature" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infiniment_petit&action=edit&section=5" title="Modifier le code source de la section : Littérature"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dans le fragment 199 des <i><a href="/wiki/Pens%C3%A9es_(Pascal)" title="Pensées (Pascal)">Pensées</a></i>, <a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Blaise Pascal</a> écrit que <span class="citation">« l’homme est infiniment éloigné de comprendre les extrêmes »</span>, coincé entre l'infiniment petit et l'infiniment grand, <span class="citation">« incapable de voir […] l’infini où il est englouti »</span>. Il imagine des mondes <a href="/wiki/Homoth%C3%A9tie" title="Homothétie">homothétiquement</a> réduits, de plus en plus petits : <span class="citation">« Qu'un ciron lui offre dans la petitesse de son corps des parties incomparablement plus petites, des jambes avec des jointures, des veines dans ces jambes, du sang dans ces veines, des humeurs dans ce sang, des gouttes dans ces humeurs, des vapeurs dans ces gouttes ; que, divisant encore ces dernières choses, il épuise ses forces en ces conceptions, et que le dernier objet où il peut arriver soit maintenant celui de notre discours ; il pensera peut-être que c'est là l'extrême petitesse de la nature. Je veux lui faire voir là dedans un abîme nouveau. Je lui veux peindre non seulement l'univers visible, mais l'immensité qu'on peut concevoir de la nature, dans l'enceinte de ce raccourci d'atome. Qu'il y voie une infinité d'univers, dont chacun a son firmament, ses planètes, sa terre, en la même proportion que le monde visible; dans cette terre, des animaux, et enfin des cirons, dans lesquels il retrouvera ce que les premiers ont donné<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>… »</span> </p><p>Dans le même ouvrage, Pascal évoque la « sphère dont le centre est partout, la circonférence nulle part »<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>, ce qui est une image traditionnelle dans la pensée occidentale, on la retrouve chez <a href="/wiki/Nicolas_de_Cues" title="Nicolas de Cues">Nicolas de Cues</a>, <a href="/wiki/Giordano_Bruno" title="Giordano Bruno">Giordano Bruno</a>, <a href="/wiki/Ma%C3%AEtre_Eckhart" title="Maître Eckhart">Maître Eckhart</a>, <a href="/wiki/Bo%C3%A8ce" title="Boèce">Boèce</a>, elle a été attribuée à <a href="/wiki/Emp%C3%A9docle" title="Empédocle">Empédocle</a>. </p> <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=Infiniment_petit&veaction=edit&section=6" 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=Infiniment_petit&action=edit&section=6" 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"><a href="/wiki/Nicolas_Bourbaki" title="Nicolas Bourbaki">N. Bourbaki</a>, <i><a href="/wiki/%C3%89l%C3%A9ments_de_math%C3%A9matique" title="Éléments de mathématique">Éléments de mathématique</a></i>, diffusion CCLS Paris 1977, <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/2-903684-03-0" title="Spécial:Ouvrages de référence/2-903684-03-0"><span class="nowrap">2-903684-03-0</span></a>)</small> p. EIV.50-51 souligne : <a href="/wiki/Jean_le_Rond_D%27Alembert" class="mw-redirect" title="Jean le Rond D'Alembert">Jean le Rond d'Alembert</a> avait pressenti <span class="citation">« que dans la <span class="citation">« métaphysique »</span> du calcul infinitésimal il n'y a rien d'autre que la notion de limite »</span> mais <span class="citation">« il ne peut, pas plus que ses contemporains, comprendre le sens véritable des développements en séries divergentes. »</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-2">↑</a> </span><span class="reference-text">Université Laval -<a rel="nofollow" class="external text" href="http://archimede.mat.ulaval.ca/amq/ancien/archives/1998/1/1998-1-part7.pdf">Jacques Lefebvre, <i>Moments et aspects de l'histoire du calcul différentiel et intégral</i></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">Pensées, Br. 72, Lafuma 199</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink noprint"><a href="#cite_ref-4">↑</a> </span><span class="reference-text">Wikisource, Pensées de Pascal, <a href="https://fr.wikisource.org/wiki/Page:%C5%92uvres_de_Blaise_Pascal,_XII.djvu/399" class="extiw" title="s:Page:Œuvres de Blaise Pascal, XII.djvu/399">section II <abbr class="abbr" title="page">p.</abbr> 73</a></span> </li> </ol></div> </div> <div class="mw-heading mw-heading2"><h2 id="Annexes">Annexes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infiniment_petit&veaction=edit&section=7" title="Modifier la section : Annexes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infiniment_petit&action=edit&section=7" title="Modifier le code source de la section : Annexes"><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="wikibooks"><a href="https://fr.wikibooks.org/wiki/Philosophie/Commentaire_du_passage_%C3%A0_propos_des_deux_infinis" class="extiw" title="b:Philosophie/Commentaire du passage à propos des deux infinis">Commentaire du passage des <i>Pensées</i> à propos des deux infinis</a>, <span class="nowrap">sur <span class="project">Wikibooks</span></span></li> </ul> </div> <div class="mw-heading mw-heading3"><h3 id="Articles_connexes">Articles connexes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infiniment_petit&veaction=edit&section=8" title="Modifier la section : Articles connexes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infiniment_petit&action=edit&section=8" title="Modifier le code source de la section : Articles connexes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a></li> <li><i><a href="/wiki/Analyse_des_infiniment_petits_pour_l%27intelligence_des_lignes_courbes" title="Analyse des infiniment petits pour l'intelligence des lignes courbes">Analyse des infiniment petits pour l'intelligence des lignes courbes</a></i>, par le <a href="/wiki/Guillaume_Fran%C3%A7ois_Antoine,_marquis_de_L%27H%C3%B4pital" title="Guillaume François Antoine, marquis de L'Hôpital">marquis de L'Hôpital</a></li> <li><a href="/wiki/Infini" title="Infini">Infini</a></li> <li><a href="/wiki/Transformation_infinit%C3%A9simale" title="Transformation infinitésimale">Transformation infinitésimale</a></li> <li><a href="/wiki/Archim%C3%A9dien" title="Archimédien">Ensemble archimédien</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Lien_externe">Lien externe</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infiniment_petit&veaction=edit&section=9" title="Modifier la section : Lien externe" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infiniment_petit&action=edit&section=9" title="Modifier le code source de la section : Lien externe"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="ouvrage"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> « <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/continuity/"><cite style="font-style:normal;" lang="en">Continuity and Infinitesimals</cite></a> », sur <span class="italique"><span class="lang-en" lang="en"><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></span></span></span>, par <a href="/wiki/John_Lane_Bell" title="John Lane Bell">John L. Bell</a></li></ul> <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 href="/wiki/Entier_relatif" title="Entier relatif">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 class="mw-selflink selflink">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:Math%C3%A9matiques" title="Portail des mathématiques"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Racine_carr%C3%A9e_bleue.svg/24px-Racine_carr%C3%A9e_bleue.svg.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Racine_carr%C3%A9e_bleue.svg/36px-Racine_carr%C3%A9e_bleue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Racine_carr%C3%A9e_bleue.svg/48px-Racine_carr%C3%A9e_bleue.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Math%C3%A9matiques" title="Portail:Mathématiques">Portail des mathématiques</a></span> </span></li> </ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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