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class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Exemples en géométrie</span> </button> <ul id="toc-Exemples_en_géométrie-sublist" class="vector-toc-list"> <li id="toc-Intersection_de_deux_droites" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Intersection_de_deux_droites"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Intersection de deux droites</span> </div> </a> <ul id="toc-Intersection_de_deux_droites-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Autres_exemples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Autres_exemples"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Autres exemples</span> </div> </a> <ul id="toc-Autres_exemples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-En_géométrie_analytique" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#En_géométrie_analytique"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>En géométrie analytique</span> </div> </a> <ul id="toc-En_géométrie_analytique-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-En_algèbre_booléenne" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#En_algèbre_booléenne"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>En algèbre booléenne</span> </div> </a> <ul id="toc-En_algèbre_booléenne-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Propriétés_algébriques" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Propriétés_algébriques"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Propriétés algébriques</span> </div> </a> <ul id="toc-Propriétés_algébriques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Intersection_d'une_famille_d'ensembles" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Intersection_d'une_famille_d'ensembles"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Intersection d'une famille d'ensembles</span> </div> </a> <ul id="toc-Intersection_d'une_famille_d'ensembles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-En_probabilités" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#En_probabilités"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>En probabilités</span> </div> </a> <ul id="toc-En_probabilités-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Articles_connexes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Articles_connexes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Articles connexes</span> </div> </a> <ul id="toc-Articles_connexes-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">Intersection (mathématiques)</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 58 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-58" 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">58 langues</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%8C%8B%E1%88%AB_%E1%88%B5%E1%89%A5%E1%88%B5%E1%89%A5" title="የጋራ ስብስብ – amharique" lang="am" hreflang="am" data-title="የጋራ ስብስብ" data-language-autonym="አማርኛ" data-language-local-name="amharique" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%82%D8%A7%D8%B7%D8%B9_(%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D9%85%D8%AC%D9%85%D9%88%D8%B9%D8%A7%D8%AA)" title="تقاطع (نظرية المجموعات) – arabe" lang="ar" hreflang="ar" data-title="تقاطع (نظرية المجموعات)" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Interseici%C3%B3n_de_conxuntos" title="Interseición de conxuntos – asturien" lang="ast" hreflang="ast" data-title="Interseición de conxuntos" data-language-autonym="Asturianu" data-language-local-name="asturien" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B0%D1%81%D1%8F%D1%87%D1%8D%D0%BD%D0%BD%D0%B5_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0%D1%9E" title="Перасячэнне мностваў – biélorusse" lang="be" hreflang="be" data-title="Перасячэнне мностваў" 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%9F%D0%B5%D1%80%D0%B0%D1%81%D1%8F%D1%87%D1%8D%D0%BD%D1%8C%D0%BD%D0%B5_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0%D1%9E" title="Перасячэньне мностваў – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Перасячэньне мностваў" 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%A1%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D0%B5_(%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%B0%D1%82%D0%B0)" title="Сечение (теория на множествата) – bulgare" lang="bg" hreflang="bg" data-title="Сечение (теория на множествата)" data-language-autonym="Български" data-language-local-name="bulgare" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Intersecci%C3%B3" title="Intersecció – catalan" lang="ca" hreflang="ca" data-title="Intersecció" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Intarsizzioni" title="Intarsizzioni – corse" lang="co" hreflang="co" data-title="Intarsizzioni" data-language-autonym="Corsu" data-language-local-name="corse" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Pr%C5%AFnik" title="Průnik – tchèque" lang="cs" hreflang="cs" data-title="Průnik" 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%99%D1%8B%D1%88%D1%81%D0%B5%D0%BD_%D1%85%C4%95%D1%80%D0%B5%D1%81%D0%BB%D0%B5%D0%BD%C4%95%D0%B2%C4%95" title="Йышсен хĕресленĕвĕ – tchouvache" lang="cv" hreflang="cv" data-title="Йышсен хĕресленĕвĕ" 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/Croestoriad_setiau" title="Croestoriad setiau – gallois" lang="cy" hreflang="cy" data-title="Croestoriad setiau" data-language-autonym="Cymraeg" data-language-local-name="gallois" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Schnittmenge" title="Schnittmenge – allemand" lang="de" hreflang="de" data-title="Schnittmenge" 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%A4%CE%BF%CE%BC%CE%AE_%CF%83%CF%85%CE%BD%CF%8C%CE%BB%CF%89%CE%BD" title="Τομή συνόλων – grec" lang="el" hreflang="el" data-title="Τομή συνόλων" 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/Intersection_(set_theory)" title="Intersection (set theory) – anglais" lang="en" hreflang="en" data-title="Intersection (set theory)" 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/Komuna%C4%B5o" title="Komunaĵo – espéranto" lang="eo" hreflang="eo" data-title="Komunaĵo" 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/Intersecci%C3%B3n_de_conjuntos" title="Intersección de conjuntos – espagnol" lang="es" hreflang="es" data-title="Intersección de conjuntos" 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/%C3%9Chisosa" title="Ühisosa – estonien" lang="et" hreflang="et" data-title="Ühisosa" 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/Ebaketa_(multzo-teoria)" title="Ebaketa (multzo-teoria) – basque" lang="eu" hreflang="eu" data-title="Ebaketa (multzo-teoria)" 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%A7%D8%B4%D8%AA%D8%B1%D8%A7%DA%A9_(%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87%E2%80%8C%D9%87%D8%A7)" title="اشتراک (نظریه مجموعه‌ها) – persan" lang="fa" hreflang="fa" data-title="اشتراک (نظریه مجموعه‌ها)" 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/Leikkaus_(matematiikka)" title="Leikkaus (matematiikka) – finnois" lang="fi" hreflang="fi" data-title="Leikkaus (matematiikka)" 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/%C3%9Ctine_osa" title="Ütine osa – võro" lang="vro" hreflang="vro" data-title="Ütine osa" data-language-autonym="Võro" data-language-local-name="võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Intersecci%C3%B3n_(conxuntos)" title="Intersección (conxuntos) – galicien" lang="gl" hreflang="gl" data-title="Intersección (conxuntos)" 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%97%D7%99%D7%AA%D7%95%D7%9A_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="חיתוך (מתמטיקה) – hébreu" lang="he" hreflang="he" data-title="חיתוך (מתמטיקה)" 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%B8%E0%A4%B0%E0%A5%8D%E0%A4%B5%E0%A4%A8%E0%A4%BF%E0%A4%B7%E0%A5%8D%E0%A4%A0_(%E0%A4%B8%E0%A4%AE%E0%A5%81%E0%A4%9A%E0%A5%8D%E0%A4%9A%E0%A4%AF_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4)" title="सर्वनिष्ठ (समुच्चय सिद्धान्त) – hindi" lang="hi" hreflang="hi" data-title="सर्वनिष्ठ (समुच्चय सिद्धान्त)" 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/Presjek_skupova" title="Presjek skupova – croate" lang="hr" hreflang="hr" data-title="Presjek skupova" data-language-autonym="Hrvatski" data-language-local-name="croate" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Metszet_(halmazelm%C3%A9let)" title="Metszet (halmazelmélet) – hongrois" lang="hu" hreflang="hu" data-title="Metszet (halmazelmélet)" data-language-autonym="Magyar" data-language-local-name="hongrois" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Intersection_(theoria_de_insimules)" title="Intersection (theoria de insimules) – interlingua" lang="ia" hreflang="ia" data-title="Intersection (theoria de insimules)" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Irisan_(teori_himpunan)" title="Irisan (teori himpunan) – indonésien" lang="id" hreflang="id" data-title="Irisan (teori himpunan)" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Sni%C3%B0mengi" title="Sniðmengi – islandais" lang="is" hreflang="is" data-title="Sniðmengi" 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/Intersezione_(insiemistica)" title="Intersezione (insiemistica) – italien" lang="it" hreflang="it" data-title="Intersezione (insiemistica)" 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/%E5%85%B1%E9%80%9A%E9%83%A8%E5%88%86_(%E6%95%B0%E5%AD%A6)" title="共通部分 (数学) – japonais" lang="ja" hreflang="ja" data-title="共通部分 (数学)" 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/%D2%9A%D0%B8%D1%8B%D0%BB%D1%8B%D1%81%D1%83" title="Қиылысу – kazakh" lang="kk" hreflang="kk" data-title="Қиылысу" 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/%EA%B5%90%EC%A7%91%ED%95%A9" title="교집합 – coréen" lang="ko" hreflang="ko" data-title="교집합" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Intersezion_(insemma)" title="Intersezion (insemma) – lombard" lang="lmo" hreflang="lmo" data-title="Intersezion (insemma)" data-language-autonym="Lombard" data-language-local-name="lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D1%81%D0%B5%D0%BA_(%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%BD%D0%B0_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%B0)" title="Пресек (теорија на множества) – macédonien" lang="mk" hreflang="mk" data-title="Пресек (теорија на множества)" data-language-autonym="Македонски" data-language-local-name="macédonien" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Doorsnede_(verzamelingenleer)" title="Doorsnede (verzamelingenleer) – néerlandais" lang="nl" hreflang="nl" data-title="Doorsnede (verzamelingenleer)" 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/Snitt_i_matematikk" title="Snitt i matematikk – norvégien nynorsk" lang="nn" hreflang="nn" data-title="Snitt i matematikk" 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/Snitt_(mengdel%C3%A6re)" title="Snitt (mengdelære) – norvégien bokmål" lang="nb" hreflang="nb" data-title="Snitt (mengdelære)" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Cz%C4%99%C5%9B%C4%87_wsp%C3%B3lna" title="Część wspólna – polonais" lang="pl" hreflang="pl" data-title="Część wspólna" 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/Ant%C3%ABrsession" title="Antërsession – piémontais" lang="pms" hreflang="pms" data-title="Antërsession" data-language-autonym="Piemontèis" data-language-local-name="piémontais" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Interse%C3%A7%C3%A3o" title="Interseção – portugais" lang="pt" hreflang="pt" data-title="Interseção" 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/Intersec%C8%9Bie_(matematic%C4%83)" title="Intersecție (matematică) – roumain" lang="ro" hreflang="ro" data-title="Intersecție (matematică)" 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%9F%D0%B5%D1%80%D0%B5%D1%81%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D0%B5_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2" title="Пересечение множеств – russe" lang="ru" hreflang="ru" data-title="Пересечение множеств" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Prienik_(matematika)" title="Prienik (matematika) – slovaque" lang="sk" hreflang="sk" data-title="Prienik (matematika)" 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/Presek_mno%C5%BEic" title="Presek množic – slovène" lang="sl" hreflang="sl" data-title="Presek množic" data-language-autonym="Slovenščina" data-language-local-name="slovène" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D1%81%D0%B5%D0%BA_(%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D1%81%D0%BA%D1%83%D0%BF%D0%BE%D0%B2%D0%B0)" title="Пресек (теорија скупова) – serbe" lang="sr" hreflang="sr" data-title="Пресек (теорија скупова)" 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/Snitt" title="Snitt – suédois" lang="sv" hreflang="sv" data-title="Snitt" data-language-autonym="Svenska" data-language-local-name="suédois" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AF%86%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%81_(%E0%AE%95%E0%AE%A3%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81)" title="வெட்டு (கணக் கோட்பாடு) – tamoul" lang="ta" hreflang="ta" data-title="வெட்டு (கணக் கோட்பாடு)" data-language-autonym="தமிழ்" data-language-local-name="tamoul" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B4%E0%B8%99%E0%B9%80%E0%B8%95%E0%B8%AD%E0%B8%A3%E0%B9%8C%E0%B9%80%E0%B8%8B%E0%B8%81%E0%B8%8A%E0%B8%B1%E0%B8%99" title="อินเตอร์เซกชัน – thaï" lang="th" hreflang="th" data-title="อินเตอร์เซกชัน" data-language-autonym="ไทย" data-language-local-name="thaï" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Salubungan_(matematika)" title="Salubungan (matematika) – tagalog" lang="tl" hreflang="tl" data-title="Salubungan (matematika)" 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/Kesi%C5%9Fme_%C3%B6zelli%C4%9Fi" title="Kesişme özelliği – turc" lang="tr" hreflang="tr" data-title="Kesişme özelliği" 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%9F%D0%B5%D1%80%D0%B5%D1%82%D0%B8%D0%BD_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD" title="Перетин множин – ukrainien" lang="uk" hreflang="uk" data-title="Перетин множин" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A9p_giao" title="Phép giao – vietnamien" lang="vi" hreflang="vi" data-title="Phép giao" 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-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BA%A4%E9%9B%86" title="交集 – wu" lang="wuu" hreflang="wuu" data-title="交集" 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%90%D0%BC%D0%B4%D0%B0%D0%BB%D2%BB%D0%B0%D0%BD" title="Амдалһан – kalmouk" lang="xal" hreflang="xal" data-title="Амдалһан" data-language-autonym="Хальмг" data-language-local-name="kalmouk" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%A4%E9%9B%86" title="交集 – chinois" lang="zh" hreflang="zh" data-title="交集" 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/%E4%BA%A4%E9%9B%86" title="交集 – chinois littéraire" lang="lzh" hreflang="lzh" data-title="交集" 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-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BA%A4%E9%9B%86" title="交集 – cantonais" lang="yue" hreflang="yue" data-title="交集" data-language-autonym="粵語" data-language-local-name="cantonais" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q185837#sitelinks-wikipedia" title="Modifier les liens interlangues" class="wbc-editpage">Modifier les liens</a></span></div> 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<div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="fr" dir="ltr"><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><p>Consultez la liste des <b>tâches à accomplir</b> en <a href="/wiki/Discussion:Intersection_(math%C3%A9matiques)" title="Discussion:Intersection (mathématiques)">page de discussion</a>. </p> </div></div> <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/Intersection" class="mw-disambig" title="Intersection">Intersection</a>. </p> </div></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Venn_A_intersect_B.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/170px-Venn_A_intersect_B.svg.png" decoding="async" width="170" height="121" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/255px-Venn_A_intersect_B.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/340px-Venn_A_intersect_B.svg.png 2x" data-file-width="350" data-file-height="250" /></a><figcaption>L'intersection des ensembles <i>A</i> et <i>B</i> est représentée dans ce <a href="/wiki/Diagrammes_d%27Euler,_de_Venn_et_de_Carroll#Diagrammes_de_Venn" title="Diagrammes d'Euler, de Venn et de Carroll">diagramme de Venn</a> par la zone violette centrale.</figcaption></figure> <p>Dans la <a href="/wiki/Th%C3%A9orie_des_ensembles" title="Théorie des ensembles">théorie des ensembles</a>, l'<b>intersection</b> est une <a href="/wiki/Op%C3%A9ration_ensembliste" title="Opération ensembliste">opération ensembliste</a> qui porte le même nom que son résultat, à savoir l'<a href="/wiki/Ensemble" title="Ensemble">ensemble</a> des éléments appartenant à la fois aux deux <a href="/wiki/Op%C3%A9rande" title="Opérande">opérandes</a> : l'intersection de deux ensembles <i>A</i> et <i>B</i> est l'ensemble, noté <span class="nowrap"><i>A</i> ∩ <i>B</i></span>, dit « <i>A</i> inter <i>B</i> », qui contient tous les éléments appartenant à la fois à <i>A</i> <b>et</b> à <i>B</i>, et seulement ceux-là. </p><p><i>A</i> et <i>B</i> sont <a href="/wiki/Ensembles_disjoints" title="Ensembles disjoints">disjoints</a> si et seulement si <span class="nowrap"><i>A</i> ∩ <i>B</i></span> est l'<a href="/wiki/Ensemble_vide" title="Ensemble vide">ensemble vide</a> ∅. </p><p><i>A</i> est <a href="/wiki/Inclusion_(math%C3%A9matiques)" title="Inclusion (mathématiques)">inclus</a> dans <i>B</i> si et seulement si <span class="nowrap"><i>A</i> ∩ <i>B</i> = <i>A</i></span>. </p><p>En <a href="/wiki/Analyse_r%C3%A9elle" title="Analyse réelle">analyse réelle</a>, les points d'intersection des <a href="/wiki/Graphe_d%27une_fonction" title="Graphe d'une fonction">courbes représentatives de deux fonctions</a> interviennent dans la description de leur <a href="/wiki/Position_relative" title="Position relative">position relative</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Exemples_en_géométrie"><span id="Exemples_en_g.C3.A9om.C3.A9trie"></span>Exemples en <a href="/wiki/G%C3%A9om%C3%A9trie" title="Géométrie">géométrie</a></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=1" title="Modifier la section : Exemples en géométrie" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=1" title="Modifier le code source de la section : Exemples en géométrie"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Intersection_(g%C3%A9om%C3%A9trie)" title="Intersection (géométrie)">Intersection (géométrie)</a>.</div></div> <div class="mw-heading mw-heading3"><h3 id="Intersection_de_deux_droites">Intersection de deux droites</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=2" title="Modifier la section : Intersection de deux droites" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=2" title="Modifier le code source de la section : Intersection de deux droites"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Dans le plan</b> </p> <ul><li>Dans le <a href="/wiki/Plan_affine" title="Plan affine">plan</a>, l'intersection de deux <a href="/wiki/Droite_(math%C3%A9matiques)" title="Droite (mathématiques)">droites</a> non <a href="/wiki/Droites_parall%C3%A8les" title="Droites parallèles">parallèles</a> est un <a href="/wiki/Point_(g%C3%A9om%C3%A9trie)" title="Point (géométrie)">point</a><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> : <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 d\cap d'=\{A\}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>∩</mo> <msup> <mi>d</mi> <mo>′</mo> </msup> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mi>A</mi> <mo fence="false" stretchy="false">}</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\cap d'=\{A\}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6127c8a31c39c3f1ffc505932309a3ed352bb9d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.515ex; height:3.009ex;" alt="{\displaystyle d\cap d'=\{A\}.}"></span> On dit qu'elles sont sécantes.</li> <li>Si deux droites sont strictement parallèles, elles n'ont pas de point commun ; leur intersection est vide : <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 d\cap d'=\varnothing .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>∩</mo> <msup> <mi>d</mi> <mo>′</mo> </msup> <mo>=</mo> <mi class="MJX-variant">∅</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\cap d'=\varnothing .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ac5046d0fed1493b4b4924fa20bd85198d06955" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.255ex; height:2.509ex;" alt="{\displaystyle d\cap d'=\varnothing .}"></span></li> <li>Si deux droites sont confondues, tous leurs points sont communs ; l'intersection est une droite : <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 d\cap d'=d=d'.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>∩</mo> <msup> <mi>d</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>d</mi> <mo>=</mo> <msup> <mi>d</mi> <mo>′</mo> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\cap d'=d=d'.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f22aade1b6ba92db6983b46051838d0511924a73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.664ex; height:2.509ex;" alt="{\displaystyle d\cap d'=d=d'.}"></span></li></ul> <p><b>Dans l'espace</b> </p> <ul><li>Si deux droites ne sont pas coplanaires <a href="/wiki/Implication_(logique)" title="Implication (logique)">alors</a> elles n'ont aucun point commun ; leur intersection est vide  : <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 d\cap d'=\varnothing .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>∩</mo> <msup> <mi>d</mi> <mo>′</mo> </msup> <mo>=</mo> <mi class="MJX-variant">∅</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\cap d'=\varnothing .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ac5046d0fed1493b4b4924fa20bd85198d06955" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.255ex; height:2.509ex;" alt="{\displaystyle d\cap d'=\varnothing .}"></span></li> <li>Deux droites parallèles ou sécantes sont coplanaires.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Autres_exemples">Autres exemples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=3" title="Modifier la section : Autres exemples" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=3" title="Modifier le code source de la section : Autres exemples"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Dans l'espace</b> </p> <ul><li>l'intersection d'une droite et d'un plan non parallèles est un point.</li> <li>l'intersection de deux plans non parallèles est une droite.</li></ul> <p><b>Dans le plan</b> </p> <ul><li>l'intersection d'une droite et d'un <a href="/wiki/Cercle" title="Cercle">cercle</a> est formée de zéro, un ou deux points, selon que la distance du centre du cercle à la droite est supérieure, égale ou inférieure au <a href="/wiki/Rayon_(g%C3%A9om%C3%A9trie)" title="Rayon (géométrie)">rayon</a> du cercle. Si l'intersection est réduite à un point, la droite est <a href="/wiki/Tangente_(g%C3%A9om%C3%A9trie)" title="Tangente (géométrie)">tangente</a> au cercle.</li> <li>l'intersection de deux cercles est formée de deux points si la distance entre leurs centres est (strictement) inférieure à la somme de leurs rayons et supérieure à leur différence, d'un point si cette distance est égale à la somme ou à la différence des rayons (cercles tangents), vide dans les autres cas<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></ul> <div class="mw-heading mw-heading2"><h2 id="En_géométrie_analytique"><span id="En_g.C3.A9om.C3.A9trie_analytique"></span>En géométrie analytique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=4" title="Modifier la section : En géométrie analytique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=4" title="Modifier le code source de la section : En géométrie analytique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <a href="/wiki/G%C3%A9om%C3%A9trie_analytique" title="Géométrie analytique">géométrie analytique</a>, l'intersection de deux objets est défini par le <a href="/wiki/Syst%C3%A8me_d%27%C3%A9quations" title="Système d'équations">système d'équations</a> formé par la réunion des <a href="/wiki/%C3%89quation" title="Équation">équations</a> associées à chaque objet. </p><p>En dimension 2, l'intersection de deux droites est définie par un système de deux équations à 2 inconnues, qui a, en général, une solution unique, sauf si son <a href="/wiki/D%C3%A9terminant_(math%C3%A9matiques)" title="Déterminant (mathématiques)">déterminant</a> est nul, auquel cas il en a soit zéro soit une infinité : on retrouve les trois cas de la géométrie. </p><p>En dimension 3, l'intersection de trois plans est définie par un système de trois équations à 3 inconnues, qui a, en général, une solution unique, sauf si son déterminant est nul. </p> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Articles détaillés : <a href="/wiki/Syst%C3%A8me_d%27%C3%A9quations_(math%C3%A9matiques_%C3%A9l%C3%A9mentaires)" class="mw-redirect" title="Système d'équations (mathématiques élémentaires)">Système d'équations (mathématiques élémentaires)</a> et <a href="/wiki/G%C3%A9om%C3%A9trie_analytique#Intersection_de_droites" title="Géométrie analytique">Géométrie analytique#Intersection de droites</a>.</div></div> <div class="mw-heading mw-heading2"><h2 id="En_algèbre_booléenne"><span id="En_alg.C3.A8bre_bool.C3.A9enne"></span>En algèbre booléenne</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=5" title="Modifier la section : En algèbre booléenne" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=5" title="Modifier le code source de la section : En algèbre booléenne"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <a href="/wiki/Alg%C3%A8bre_de_Boole_(structure)" title="Algèbre de Boole (structure)">algèbre booléenne</a>, l'intersection est associée à l'<a href="/wiki/Connecteur_logique" title="Connecteur logique">opérateur logique</a> <code>et</code> : si <i>A</i> est l'ensemble des éléments de <i>E</i> possédant la propriété P (ou satisfaisant la condition P) et <i>B</i> l'ensemble des éléments de <i>E</i> possédant la propriété Q (ou satisfaisant la condition Q ), alors <i>A</i> ∩ <i>B</i> est l'ensemble des éléments de E possédant la propriété P<code>et</code>Q (ou satisfaisant à la fois la condition P et la condition Q ). </p><p>Exemple 1 : si <i>E</i> est l'ensemble des <a href="/wiki/Entier_naturel" title="Entier naturel">entiers naturels</a> inférieurs à 10, <i>A</i> l'ensemble des éléments de <i>E</i> impairs, et <i>B</i> l'ensemble des éléments de <i>E</i> premiers, alors <i>A</i> ∩ <i>B</i> est l'ensemble des éléments de <i>E</i> impairs <b>et</b> premiers : </p> <dl><dd><i>A</i> = {1, 3, 5, 7, 9} , <i>B</i> = {2, 3, 5, 7}, <i>A</i> ∩ <i>B</i> = {3, 5, 7}.</dd></dl> <p>Exemple 2 : l'intersection de l'ensemble des <a href="/wiki/Rectangle" title="Rectangle">rectangles</a> (<a href="/wiki/Quadrilat%C3%A8re" title="Quadrilatère">quadrilatères</a> ayant leurs quatre angles droits) et de l'ensemble des <a href="/wiki/Losange" title="Losange">losanges</a> (quadrilatères ayant leurs quatre côtés égaux) est l'ensemble des <a href="/wiki/Carr%C3%A9" title="Carré">carrés</a> (quadrilatères ayant leurs quatre angles droits <b>et</b> leurs quatre côtés égaux). </p><p>On définit de même l'intersection d'une <a href="/wiki/Classe_(math%C3%A9matiques)" title="Classe (mathématiques)">classe</a> quelconque d'ensembles (non nécessairement réduite à deux ensembles, ni même finie, ni même <a href="/wiki/Famille_(math%C3%A9matiques)" title="Famille (mathématiques)">indexée</a> par un ensemble : on demande seulement qu'elle soit non vide). </p> <div class="mw-heading mw-heading2"><h2 id="Propriétés_algébriques"><span id="Propri.C3.A9t.C3.A9s_alg.C3.A9briques"></span>Propriétés algébriques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=6" title="Modifier la section : Propriétés algébriques" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=6" title="Modifier le code source de la section : Propriétés algébriques"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>L'intersection est <a href="/wiki/Associativit%C3%A9" title="Associativité">associative</a>, c'est-à-dire que, pour des ensembles <i>A</i>, <i>B</i> et <i>C</i> quelconques, on a :<br />(<i>A</i> ∩ <i>B</i>) ∩ <i>C</i> = <i>A</i> ∩ (<i>B</i> ∩ <i>C</i>).</li> <li>L'intersection est <a href="/wiki/Commutativit%C3%A9" class="mw-redirect" title="Commutativité">commutative</a>, c'est-à-dire que, pour des ensembles <i>A</i> et <i>B</i> quelconques, on a :<br /><i>A</i> ∩ <i>B</i> = <i>B</i> ∩ <i>A</i>.</li> <li>L'<a href="/wiki/Union_(math%C3%A9matiques)" title="Union (mathématiques)">union</a> est <a href="/wiki/Distributivit%C3%A9" title="Distributivité">distributive</a> sur l'intersection, c'est-à-dire que, pour des ensembles <i>A</i>, <i>B</i> et <i>C</i> quelconques, on a :<br /><i>A</i> ∪ (<i>B</i> ∩ <i>C</i>) = (<i>A</i> ∪ <i>B</i>) ∩ (<i>A</i> ∪ <i>C</i>).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Intersection_d'une_famille_d'ensembles"><span id="Intersection_d.27une_famille_d.27ensembles"></span>Intersection d'une famille d'ensembles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=7" title="Modifier la section : Intersection d'une famille d'ensembles" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=7" title="Modifier le code source de la section : Intersection d'une famille d'ensembles"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Alg%C3%A8bre_des_parties_d%27un_ensemble#Réunion_et_intersection_:_cas_général" title="Algèbre des parties d'un ensemble">Algèbre des parties d'un ensemble, § « Réunion et intersection : cas général »</a>.</div></div> <p>On généralise ce concept à une <a href="/wiki/Famille_(math%C3%A9matiques)" title="Famille (mathématiques)">famille</a> d'ensembles (<i>E<sub>i</sub></i>)<sub><i>i</i>∈<i>I</i></sub> (non nécessairement réduite à deux ensembles, ni même finie). L'intersection des <i>E<sub>i</sub></i>, notée ∩<sub><i>i</i>∈<i>I</i></sub> <i>E<sub>i</sub></i>, est l'ensemble des éléments communs à tous les <i>E<sub>i</sub></i> (si <i>I</i> est l'<a href="/wiki/Ensemble_vide" title="Ensemble vide">ensemble vide</a>, cette intersection n'est donc pas définie dans l'absolu). </p><p>Formellement : </p> <center><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 \forall x,\quad x\in \bigcap _{i\in I}E_{i}\Leftrightarrow (\forall i\in I,\ x\in E_{i}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>,</mo> <mspace width="1em" /> <mi>x</mi> <mo>∈</mo> <munder> <mo>⋂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </munder> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">⇔</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∀</mi> <mi>i</mi> <mo>∈</mo> <mi>I</mi> <mo>,</mo> <mtext> </mtext> <mi>x</mi> <mo>∈</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x,\quad x\in \bigcap _{i\in I}E_{i}\Leftrightarrow (\forall i\in I,\ x\in E_{i}).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27be4f232c313334cd2a97f338860bd9528cfe7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:36.11ex; height:5.676ex;" alt="{\displaystyle \forall x,\quad x\in \bigcap _{i\in I}E_{i}\Leftrightarrow (\forall i\in I,\ x\in E_{i}).}"></span></center> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="En_probabilités"><span id="En_probabilit.C3.A9s"></span>En probabilités</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=8" title="Modifier la section : En probabilités" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=8" title="Modifier le code source de la section : En probabilités"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>On appelle <b>intersection</b> de deux évènements<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> A et B, l’événement qui est réalisé si et seulement si A <b>et</b> B le sont.<br />C’est un événement noté 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 \cap }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \cap }"></span> B. <br />L’intersection correspond à la <i>conjonction</i> logique «  <b>A et B</b> ». </p><p><i><u>Exemple avec le jeté de dés 6 faces</u></i>: </p><p>En jetant un dé, celui ci tombe sur l'une des 6 faces. L'univers des événements possible est : <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 \Omega =\{1,2,3,4,5,6\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>6</mn> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega =\{1,2,3,4,5,6\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e70d20610a1d056140fb7c143dcfae4bfda1465" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.246ex; height:2.843ex;" alt="{\displaystyle \Omega =\{1,2,3,4,5,6\}}"></span>.<br /> Considérons l'événement A : l<i>e dé tombe sur une face paire</i> et l'événement B : <i>le dé tombe sur une face impaire.</i> </p><p>L'événement <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 A\cap B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∩</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\cap B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb27b38cf9eac6060e67b61f66cd9beec5067f81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\cap B}"></span> ne se produira évidemment jamais on l'appelle <b>événement impossible,</b> il est 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 \varnothing }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">∅</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varnothing }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00595c5e33692e724937fdcc8870496acce1ac74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.009ex;" alt="{\displaystyle \varnothing }"></span><br /> </p><p>Considérons maintenant les événements A <i>le dé tombe sur une face inférieure à 5</i> et B <i>le dé tombe sur une face supérieure à 2.</i> L'événement <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 A\cap B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∩</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\cap B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb27b38cf9eac6060e67b61f66cd9beec5067f81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\cap B}"></span> se produit lorsque le dé tombe sur une face inférieure à 5 et supérieure à 2 soit 3 ou 4 : </p><p><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 A\cap B=\{3,4\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∩</mo> <mi>B</mi> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\cap B=\{3,4\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7c5f11148f7d8b3088761578c6d68c5ce286eba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.872ex; height:2.843ex;" alt="{\displaystyle A\cap B=\{3,4\}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=9" title="Modifier la section : Notes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&action=edit&section=9" title="Modifier le code source de la section : Notes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <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">Pour être rigoureux, on devrait dire ici : « est un <a href="/wiki/Singleton_(math%C3%A9matiques)" title="Singleton (mathématiques)">singleton</a> » ; l'abus « est un point » est considéré comme acceptable.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-2">↑</a> </span><span class="reference-text">Pour le démontrer, il suffit de supposer les cercles, centrés en A et B, sécants en M, et d'écrire les <a href="/wiki/In%C3%A9galit%C3%A9_triangulaire" title="Inégalité triangulaire">inégalités triangulaires</a> dans le triangle ABM.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink noprint"><a href="#cite_ref-3">↑</a> </span><span class="reference-text"><span class="ouvrage">« <a rel="nofollow" class="external text" href="https://mathsv.univ-lyon1.fr/app/cours/?theme=proba&chap=2"><cite style="font-style:normal;">MathSV : affichage des cours en ligne</cite></a> », sur <span class="italique">mathsv.univ-lyon1.fr</span> <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2024-02-18" data-sort-value="2024-02-18">18 février 2024</time>)</small></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Articles_connexes">Articles connexes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Intersection_(math%C3%A9matiques)&veaction=edit&section=10" 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=Intersection_(math%C3%A9matiques)&action=edit&section=10" 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/Union_(math%C3%A9matiques)" title="Union (mathématiques)">Union (mathématiques)</a></li> <li><a href="/wiki/Alg%C3%A8bre_des_parties_d%27un_ensemble" title="Algèbre des parties d'un ensemble">Algèbre des parties d'un ensemble</a></li> <li><a href="/wiki/Diagramme_de_Venn" title="Diagramme de Venn">Diagramme de Venn</a></li></ul> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint collapsed" style=""> <tbody><tr><th class="navbox-title" colspan="2" 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_Op%C3%A9rations_binaires" title="Modèle:Palette Opérations binaires"><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_Op%C3%A9rations_binaires&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%"><a href="/wiki/Op%C3%A9ration_binaire" title="Opération binaire">Opérations binaires</a></div></th> </tr> <tr> <td class="navbox-list" style="" colspan="2"><table class="navbox-columns-table" style="text-align:left;margin:0px;width:100%;"><tbody><tr><td class="navbox-abovebelow" colspan="1" style="background-color: #DFE0FF; text-align: center;"><b>Numériques</b></td><td class="navbox-abovebelow" colspan="1" style="background-color: #DFE0FF; text-align: center;"><b>En ensemble ordonné</b></td><td class="navbox-abovebelow" colspan="1" style="background-color: #DFE0FF; text-align: center;"><b>Structurelles</b></td><td class="navbox-abovebelow" colspan="1" style="background-color: #DFE0FF; text-align: center;"><b>Autres</b></td></tr><tr style="vertical-align:top;"><td rowspan="" colspan="" style="padding:0px;;;width:10em;"><div> <p><b>Élémentaires</b><br /><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 +}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle +}"></span> <a href="/wiki/Addition" title="Addition">Addition</a><br /><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 -}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04bd52ce670743d3b61bec928a7ec9f47309eb36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle -}"></span> <a href="/wiki/Soustraction" title="Soustraction">Soustraction</a><br /><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 \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span> <a href="/wiki/Multiplication" title="Multiplication">Multiplication</a><br /><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 \div }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>÷</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \div }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/837b35ee5d25b5ce7b07f292c27cc90533dd9fd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle \div }"></span> <a href="/wiki/Division" title="Division">Division</a><br /><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 {\hat {}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow /> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97daf05d8be90237eb4d2e4a46d3733ca829bd1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.162ex; height:2.009ex;" alt="{\displaystyle {\hat {}}}"></span> <a href="/wiki/Puissance_d%27un_nombre" title="Puissance d'un nombre">Puissance</a> </p><p><b>Arithmétiques</b><br /><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 \mathrm {div} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {div} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b2d000acb2863a923fa83e5bee0635410b909bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.167ex; height:2.176ex;" alt="{\displaystyle \mathrm {div} }"></span> <a href="/wiki/Division_euclidienne" title="Division euclidienne">Quotient euclidien</a><br /><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 \mathrm {mod} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">d</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {mod} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d75a50b3797e46642fd900093e002af888607a78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.391ex; height:2.176ex;" alt="{\displaystyle \mathrm {mod} }"></span> <a href="/wiki/Reste" title="Reste">Reste euclidien</a><br /><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 \mathrm {pgcd} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">d</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {pgcd} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a99af40437989ee3ff61087ef6784068cc7d1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.78ex; height:2.509ex;" alt="{\displaystyle \mathrm {pgcd} }"></span> <a href="/wiki/Plus_grand_commun_diviseur" title="Plus grand commun diviseur">PGCD</a><br /><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 \mathrm {ppcm} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {ppcm} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2414692d872334199729ef7ec1ee384b8a57f0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.553ex; height:2.009ex;" alt="{\displaystyle \mathrm {ppcm} }"></span> <a href="/wiki/Plus_petit_commun_multiple" title="Plus petit commun multiple">PPCM</a> </p><p><b>Combinatoires</b><br /><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 ()}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ()}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7bc8aa05e1302397bb3e7877e842784991351df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.843ex;" alt="{\displaystyle ()}"></span> <a href="/wiki/Coefficient_binomial" title="Coefficient binomial">Coefficient binomial</a><br /><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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> <a href="/wiki/Arrangement" title="Arrangement">Arrangement</a> </p> </div></td><td rowspan="" colspan="" style="padding:0px;;;width:10em;"><div> <p><b>Ensembles de parties</b><br /><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 \cup }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∪</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cup }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8ff7d0293ad19b43524a133ae5129f3d71f2040" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \cup }"></span> <a href="/wiki/Union_(math%C3%A9matiques)" title="Union (mathématiques)">Union</a><br /><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 \backslash }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant" mathvariant="normal">∖</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \backslash }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e865e5b244a7a5d4fdf7a95fe4cea6d25e581ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.162ex; height:2.843ex;" alt="{\displaystyle \backslash }"></span> <a href="/wiki/Alg%C3%A8bre_des_parties_d%27un_ensemble#Difference" title="Algèbre des parties d'un ensemble">Différence</a><br /><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 \cap }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \cap }"></span> <a class="mw-selflink selflink">Intersection</a><br /><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 \Delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32769037c408874e1890f77554c65f39c523ebe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \Delta }"></span> <a href="/wiki/Alg%C3%A8bre_des_parties_d%27un_ensemble#Difference_symetrique" title="Algèbre des parties d'un ensemble">Différence symétrique</a> </p><p><b>Ordre total</b><br /><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 \min }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">min</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \min }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/695d28931288a686335c3969dfd15bb76ea873db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.875ex; height:2.176ex;" alt="{\displaystyle \min }"></span> <a href="/wiki/Extremum" title="Extremum">Minimum</a><br /><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 \max }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">max</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \max }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8e49fca3e322708b32d21eaa8b095dc05f09538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.326ex; height:1.676ex;" alt="{\displaystyle \max }"></span> <a href="/wiki/Extremum" title="Extremum">Maximum</a> </p><p><b>Treillis</b><br /><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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> <a href="/wiki/Treillis_(ensemble_ordonn%C3%A9)" title="Treillis (ensemble ordonné)">Borne inférieure</a><br /><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 \vee }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vee }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b76220c6805c9b465d6efbc7686c624f49f3023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \vee }"></span> <a href="/wiki/Treillis_(ensemble_ordonn%C3%A9)" title="Treillis (ensemble ordonné)">Borne supérieure</a> </p> </div></td><td rowspan="" colspan="" style="padding:0px;;;width:10em;"><div> <div style="column-count:2;column-gap:1em;text-align:center" class="colonnes"> <p><b>Ensembles</b><br /><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 \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span> <a href="/wiki/Produit_cart%C3%A9sien" title="Produit cartésien">Produit cartésien</a><br /><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 {\dot {\cup }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>∪</mo> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\cup }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ca2f2880f761544ce268abf4057fcc1f50c0e12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.509ex;" alt="{\displaystyle {\dot {\cup }}}"></span> <a href="/wiki/Op%C3%A9ration_ensembliste#Somme_disjointe" title="Opération ensembliste">Somme disjointe</a><br /><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 {\hat {}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow /> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97daf05d8be90237eb4d2e4a46d3733ca829bd1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.162ex; height:2.009ex;" alt="{\displaystyle {\hat {}}}"></span> <a href="/wiki/Op%C3%A9ration_ensembliste#Exponentiation" title="Opération ensembliste">Puissance ensembliste</a> </p><p><b>Groupes</b><br /><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 \oplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b16e2bdaefee9eed86d866e6eba3ac47c710f60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \oplus }"></span> <a href="/wiki/Somme_directe" title="Somme directe">Somme directe</a><br /><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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> <a href="/wiki/Produit_libre" title="Produit libre">Produit libre</a><br /><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 \wr }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≀</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wr }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b4cda60813dda84640dc58dc142774abfa5a07d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:0.647ex; height:2.176ex;" alt="{\displaystyle \wr }"></span> <a href="/wiki/Produit_en_couronne" title="Produit en couronne">Produit en couronne</a> </p><p><b>Modules</b><br /><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 \otimes }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \otimes }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de29098f5a34ee296a505681a0d5e875070f2aea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \otimes }"></span> <a href="/wiki/Produit_tensoriel" title="Produit tensoriel">Produit tensoriel</a><br /><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 \mathrm {Hom} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Hom} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eea3aafc91ebbd147d45c3c69e88431c48cbe9f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.841ex; height:2.176ex;" alt="{\displaystyle \mathrm {Hom} }"></span> <a href="/wiki/Foncteur_Hom" title="Foncteur Hom">Homomorphisme</a><br /><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 \mathrm {Tor} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Tor} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab99a129c5d7d0c5726c68a87fff94e73a0d57fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.752ex; height:2.176ex;" alt="{\displaystyle \mathrm {Tor} }"></span> <a href="/wiki/Foncteur_Tor" title="Foncteur Tor">Torsion</a><br /><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 \mathrm {Ext} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">t</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Ext} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d62c5fa7a8cff017d6febd4d585be1f0bcd2799" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.715ex; height:2.176ex;" alt="{\displaystyle \mathrm {Ext} }"></span> <a href="/wiki/Foncteur_Ext" title="Foncteur Ext">Extension</a> </p><p><b>Arbres</b><br /><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 \vee }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vee }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b76220c6805c9b465d6efbc7686c624f49f3023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \vee }"></span> <a href="/w/index.php?title=Enracinement_(math%C3%A9matiques)&action=edit&redlink=1" class="new" title="Enracinement (mathématiques) (page inexistante)">Enracinement</a> </p><p><b>Variétés connexes</b><br /><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 \#}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">#</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \#}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f72e8254fd59fa4060c66c9310acbaf6df2ce894" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.936ex; height:2.509ex;" alt="{\displaystyle \#}"></span> <a href="/wiki/Somme_connexe" title="Somme connexe">Somme connexe</a> </p><p><b>Espaces pointés</b><br /><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 \vee }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vee }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b76220c6805c9b465d6efbc7686c624f49f3023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \vee }"></span> <a href="/wiki/Bouquet_(math%C3%A9matiques)" title="Bouquet (mathématiques)">Bouquet</a><br /><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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> <a href="/wiki/Smash-produit" title="Smash-produit">Smash-produit</a><br /><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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> <a href="/wiki/Joint_(math%C3%A9matiques)" title="Joint (mathématiques)">Joint</a> </p> </div> </div></td><td rowspan="" colspan="" style="padding:0px;;;width:10em;"><div> <div style="column-count:2;column-gap:1em;text-align:center" class="colonnes"> <p><b>Fonctionnelles</b><br /><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 \circ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∘</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \circ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99add39d2b681e2de7ff62422c32704a05c7ec31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.125ex; margin-bottom: -0.297ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \circ }"></span> <a href="/wiki/Composition_de_fonctions" title="Composition de fonctions">Composition de fonctions</a><br /><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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> <a href="/wiki/Produit_de_convolution" title="Produit de convolution">Produit de convolution</a> </p><p><b>Vectorielles</b><br /><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 \cdot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⋅</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cdot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba2c023bad1bd39ed49080f729cbf26bc448c9ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.439ex; margin-bottom: -0.61ex; width:0.647ex; height:1.176ex;" alt="{\displaystyle \cdot }"></span> <a href="/wiki/Produit_scalaire" title="Produit scalaire">Produit scalaire</a><br /><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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> <a href="/wiki/Produit_vectoriel" title="Produit vectoriel">Produit vectoriel</a><br /><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 \times \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59549550bdbbf3ee3c3e699ef776a2fb75d925b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.195ex; height:1.509ex;" alt="{\displaystyle \times \,}"></span> <a href="/wiki/Produit_vectoriel_en_dimension_7" title="Produit vectoriel en dimension 7">Produit vectoriel généralisé</a> </p><p><b>Algébriques</b><br /><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 [,]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mo>,</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [,]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f04349be7aa458edb6f1ab423189a8455c6e21f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.328ex; height:2.843ex;" alt="{\displaystyle [,]}"></span> <a href="/wiki/Crochet_de_Lie" title="Crochet de Lie">Crochet de Lie</a><br /><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 \{,\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mo>,</mo> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{,\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e6e62f0d087cac84c136e76f9c5e8c9f6af5f3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.359ex; height:2.843ex;" alt="{\displaystyle \{,\}}"></span> <a href="/wiki/Crochet_de_Poisson" title="Crochet de Poisson">Crochet de Poisson</a><br /><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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> <a href="/wiki/Produit_ext%C3%A9rieur" title="Produit extérieur">Produit extérieur</a> </p><p><b>Homologiques</b><br /><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 \smile }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⌣</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \smile }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3885eca63e224e40912ea2b44c5fe85f3d4f8be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.309ex; margin-bottom: -0.48ex; width:2.324ex; height:1.343ex;" alt="{\displaystyle \smile }"></span> <a href="/wiki/Cup-produit" title="Cup-produit">Cup-produit</a><br /><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 \cdot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⋅</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cdot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba2c023bad1bd39ed49080f729cbf26bc448c9ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.439ex; margin-bottom: -0.61ex; width:0.647ex; height:1.176ex;" alt="{\displaystyle \cdot }"></span> <a href="/w/index.php?title=Produit_d%27intersection&action=edit&redlink=1" class="new" title="Produit d'intersection (page inexistante)">Produit d'intersection</a> </p><p><b>Séquentielles</b><br /><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 +}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle +}"></span> <a href="/wiki/Concat%C3%A9nation" title="Concaténation">Concaténation</a> </p> </div> </div></td></tr></tbody></table></td> </tr> <tr> <td class="navbox-banner" style="background-color:transparent; color:inherit;" colspan="2"><div class="liste-horizontale"><b>Logique booléenne</b> : <ul><li><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 \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> <a href="/wiki/Fonction_ET" title="Fonction ET">ET (conjonction)</a></li> <li><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 \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> <a href="/wiki/Fonction_OU" title="Fonction OU">OU (disjonction)</a></li> <li><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 \oplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b16e2bdaefee9eed86d866e6eba3ac47c710f60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \oplus }"></span> <a href="/wiki/Fonction_OU_exclusif" title="Fonction OU exclusif">OU exclusif</a></li> <li><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 \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span> <a href="/wiki/Implication_(logique)" title="Implication (logique)">IMP (implication)</a></li> <li><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 \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span> <a href="/wiki/%C3%89quivalence_logique" title="Équivalence logique">EQV (équivalence)</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" alt="" width="1" height="1" style="border: none; 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