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data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Innhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Til toppen)</div> </a> </li> <li id="toc-Formell_definisjon" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formell_definisjon"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Formell definisjon</span> </div> </a> <ul id="toc-Formell_definisjon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eksempler" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksempler"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Eksempler</span> </div> </a> <button aria-controls="toc-Eksempler-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underseksjonen Eksempler</span> </button> <ul id="toc-Eksempler-sublist" class="vector-toc-list"> <li id="toc-Aritmetikk" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aritmetikk"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Aritmetikk</span> </div> </a> <ul id="toc-Aritmetikk-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Matematikk_generelt" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Matematikk_generelt"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Matematikk generelt</span> </div> </a> <ul id="toc-Matematikk_generelt-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Assosiativitet_i_matematiske_strukturer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Assosiativitet_i_matematiske_strukturer"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Assosiativitet i matematiske strukturer</span> </div> </a> <ul id="toc-Assosiativitet_i_matematiske_strukturer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Se_også" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_også"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Se også</span> </div> </a> <ul id="toc-Se_også-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referanser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referanser"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Litteratur" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Litteratur"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Litteratur</span> </div> </a> <ul id="toc-Litteratur-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="Innhold" 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="Vis/skjul innholdsfortegnelsen" > <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">Vis/skjul innholdsfortegnelsen</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">Assosiativ lov</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="Gå til en artikkel på et annet språk. Tilgjengelig på 67 språk" > <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-67" 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">67 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Assosiativitet" title="Assosiativitet – norsk nynorsk" lang="nn" hreflang="nn" data-title="Assosiativitet" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Associativitet" title="Associativitet – dansk" lang="da" hreflang="da" data-title="Associativitet" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Associativitet" title="Associativitet – svensk" lang="sv" hreflang="sv" data-title="Associativitet" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Tengiregla" title="Tengiregla – islandsk" lang="is" hreflang="is" data-title="Tengiregla" data-language-autonym="Íslenska" data-language-local-name="islandsk" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D9%85%D9%84%D9%8A%D8%A9_%D8%AA%D8%AC%D9%85%D9%8A%D8%B9%D9%8A%D8%A9" title="عملية تجميعية – arabisk" lang="ar" hreflang="ar" data-title="عملية تجميعية" data-language-autonym="العربية" data-language-local-name="arabisk" 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/Asociativid%C3%A1" title="Asociatividá – asturisk" lang="ast" hreflang="ast" data-title="Asociatividá" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%D1%8B%D2%A1_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Ассоциативлыҡ (математика) – basjkirsk" lang="ba" hreflang="ba" data-title="Ассоциативлыҡ (математика)" data-language-autonym="Башҡортса" data-language-local-name="basjkirsk" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D1%81%D0%B0%D1%86%D1%8B%D1%8F%D1%82%D1%8B%D1%9E%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%8B%D1%8F" title="Асацыятыўная аперацыя – belarusisk" lang="be" hreflang="be" data-title="Асацыятыўная аперацыя" data-language-autonym="Беларуская" data-language-local-name="belarusisk" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Асоциативност – bulgarsk" lang="bg" hreflang="bg" data-title="Асоциативност" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Asocijativnost" title="Asocijativnost – bosnisk" lang="bs" hreflang="bs" data-title="Asocijativnost" data-language-autonym="Bosanski" data-language-local-name="bosnisk" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Propietat_associativa" title="Propietat associativa – katalansk" lang="ca" hreflang="ca" data-title="Propietat associativa" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D1%81%D1%81%D0%B0%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%C4%83%D1%85_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Ассациативлăх (математика) – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Ассациативлăх (математика)" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Asociativita" title="Asociativita – tsjekkisk" lang="cs" hreflang="cs" data-title="Asociativita" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Assoziativgesetz" title="Assoziativgesetz – tysk" lang="de" hreflang="de" data-title="Assoziativgesetz" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Assotsiatiivsus" title="Assotsiatiivsus – estisk" lang="et" hreflang="et" data-title="Assotsiatiivsus" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%81%CE%BF%CF%83%CE%B5%CF%84%CE%B1%CE%B9%CF%81%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE_%CE%B9%CE%B4%CE%B9%CF%8C%CF%84%CE%B7%CF%84%CE%B1" title="Προσεταιριστική ιδιότητα – gresk" lang="el" hreflang="el" data-title="Προσεταιριστική ιδιότητα" data-language-autonym="Ελληνικά" data-language-local-name="gresk" 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/Associative_property" title="Associative property – engelsk" lang="en" hreflang="en" data-title="Associative property" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Asociatividad_(%C3%A1lgebra)" title="Asociatividad (álgebra) – spansk" lang="es" hreflang="es" data-title="Asociatividad (álgebra)" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Asocieco" title="Asocieco – esperanto" lang="eo" hreflang="eo" data-title="Asocieco" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Elkarkortasun" title="Elkarkortasun – baskisk" lang="eu" hreflang="eu" data-title="Elkarkortasun" data-language-autonym="Euskara" data-language-local-name="baskisk" 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%AE%D8%A7%D8%B5%DB%8C%D8%AA_%D8%B4%D8%B1%DA%A9%D8%AA%E2%80%8C%D9%BE%D8%B0%DB%8C%D8%B1%DB%8C" title="خاصیت شرکت‌پذیری – persisk" lang="fa" hreflang="fa" data-title="خاصیت شرکت‌پذیری" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Associativit%C3%A9" title="Associativité – fransk" lang="fr" hreflang="fr" data-title="Associativité" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Oibr%C3%ADocht_chomhthiomsaitheach" title="Oibríocht chomhthiomsaitheach – irsk" lang="ga" hreflang="ga" data-title="Oibríocht chomhthiomsaitheach" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Asociatividade_(%C3%A1lxebra)" title="Asociatividade (álxebra) – galisisk" lang="gl" hreflang="gl" data-title="Asociatividade (álxebra)" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B2%B0%ED%95%A9%EB%B2%95%EC%B9%99" title="결합법칙 – koreansk" lang="ko" hreflang="ko" data-title="결합법칙" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B6%D5%B8%D6%82%D5%A3%D5%B8%D6%80%D5%A4%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Զուգորդականություն – armensk" lang="hy" hreflang="hy" data-title="Զուգորդականություն" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Asocijativnost" title="Asocijativnost – kroatisk" lang="hr" hreflang="hr" data-title="Asocijativnost" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sifat_asosiatif" title="Sifat asosiatif – indonesisk" lang="id" hreflang="id" data-title="Sifat asosiatif" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Associativitate" title="Associativitate – interlingua" lang="ia" hreflang="ia" data-title="Associativitate" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Associativit%C3%A0" title="Associatività – italiensk" lang="it" hreflang="it" data-title="Associatività" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%A2%D7%95%D7%9C%D7%94_%D7%90%D7%A1%D7%95%D7%A6%D7%99%D7%90%D7%98%D7%99%D7%91%D7%99%D7%AA" title="פעולה אסוציאטיבית – hebraisk" lang="he" hreflang="he" data-title="פעולה אסוציאטיבית" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D1%82%D1%96%D0%BA_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Ассоциативтік операция – kasakhisk" lang="kk" hreflang="kk" data-title="Ассоциативтік операция" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Associativitas_(mathematica)" title="Associativitas (mathematica) – latin" lang="la" hreflang="la" data-title="Associativitas (mathematica)" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Asociativit%C4%81te" title="Asociativitāte – latvisk" lang="lv" hreflang="lv" data-title="Asociativitāte" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Asociatyvumas" title="Asociatyvumas – litauisk" lang="lt" hreflang="lt" data-title="Asociatyvumas" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Asszociativit%C3%A1s" title="Asszociativitás – ungarsk" lang="hu" hreflang="hu" data-title="Asszociativitás" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D1%81%D0%BE%D1%86%D0%B8%D1%98%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Асоцијативност – makedonsk" lang="mk" hreflang="mk" data-title="Асоцијативност" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%BE%E0%B4%B9%E0%B4%9A%E0%B4%B0%E0%B5%8D%E0%B4%AF%E0%B4%A8%E0%B4%BF%E0%B4%AF%E0%B4%AE%E0%B4%82" title="സാഹചര്യനിയമം – malayalam" lang="ml" hreflang="ml" data-title="സാഹചര്യനിയമം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kalis_sekutuan" title="Kalis sekutuan – malayisk" lang="ms" hreflang="ms" data-title="Kalis sekutuan" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Associativiteit_(wiskunde)" title="Associativiteit (wiskunde) – nederlandsk" lang="nl" hreflang="nl" data-title="Associativiteit (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B5%90%E5%90%88%E6%B3%95%E5%89%87" title="結合法則 – japansk" lang="ja" hreflang="ja" data-title="結合法則" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Asotsiatiifgesets" title="Asotsiatiifgesets – nordfrisisk" lang="frr" hreflang="frr" data-title="Asotsiatiifgesets" data-language-autonym="Nordfriisk" data-language-local-name="nordfrisisk" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Associativitat" title="Associativitat – oksitansk" lang="oc" hreflang="oc" data-title="Associativitat" data-language-autonym="Occitan" data-language-local-name="oksitansk" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Assotsiativlik" title="Assotsiativlik – usbekisk" lang="uz" hreflang="uz" data-title="Assotsiativlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%C5%81%C4%85czno%C5%9B%C4%87_(matematyka)" title="Łączność (matematyka) – polsk" lang="pl" hreflang="pl" data-title="Łączność (matematyka)" data-language-autonym="Polski" data-language-local-name="polsk" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Associatividade" title="Associatividade – portugisisk" lang="pt" hreflang="pt" data-title="Associatividade" data-language-autonym="Português" data-language-local-name="portugisisk" 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/Asociativitate" title="Asociativitate – rumensk" lang="ro" hreflang="ro" data-title="Asociativitate" data-language-autonym="Română" data-language-local-name="rumensk" 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%90%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D1%8C_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Ассоциативность (математика) – russisk" lang="ru" hreflang="ru" data-title="Ассоциативность (математика)" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Vetia_e_shoq%C3%ABrimit" title="Vetia e shoqërimit – albansk" lang="sq" hreflang="sq" data-title="Vetia e shoqërimit" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Associativity" title="Associativity – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Associativity" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Asociat%C3%ADvnos%C5%A5" title="Asociatívnosť – slovakisk" lang="sk" hreflang="sk" data-title="Asociatívnosť" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" 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/Asociativnost" title="Asociativnost – slovensk" lang="sl" hreflang="sl" data-title="Asociativnost" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DB%8C%DB%95%DA%A9%D8%AA%D8%B1%D8%A8%DB%95%D8%B3%D8%AA%D9%86" title="یەکتربەستن – sentralkurdisk" lang="ckb" hreflang="ckb" data-title="یەکتربەستن" data-language-autonym="کوردی" data-language-local-name="sentralkurdisk" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D1%81%D0%BE%D1%86%D0%B8%D1%98%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Асоцијативност – serbisk" lang="sr" hreflang="sr" data-title="Асоцијативност" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Asocijativnost" title="Asocijativnost – serbokroatisk" lang="sh" hreflang="sh" data-title="Asocijativnost" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Liit%C3%A4nn%C3%A4isyys" title="Liitännäisyys – finsk" lang="fi" hreflang="fi" data-title="Liitännäisyys" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%87%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%AA%E0%AF%8D_%E0%AE%AA%E0%AE%A3%E0%AF%8D%E0%AE%AA%E0%AF%81" title="சேர்ப்புப் பண்பு – tamil" lang="ta" hreflang="ta" data-title="சேர்ப்புப் பண்பு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%D1%8B%D0%BA" title="Ассоциативлык – tatarisk" lang="tt" hreflang="tt" data-title="Ассоциативлык" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarisk" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%9A%E0%B8%B1%E0%B8%95%E0%B8%B4%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%80%E0%B8%9B%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%99%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88" title="สมบัติการเปลี่ยนหมู่ – thai" lang="th" hreflang="th" data-title="สมบัติการเปลี่ยนหมู่" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Birle%C5%9Fme_%C3%B6zelli%C4%9Fi_(ikili_i%C5%9Flemler)" title="Birleşme özelliği (ikili işlemler) – tyrkisk" lang="tr" hreflang="tr" data-title="Birleşme özelliği (ikili işlemler)" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" 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%90%D1%81%D0%BE%D1%86%D1%96%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Асоціативність – ukrainsk" lang="uk" hreflang="uk" data-title="Асоціативність" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Propiet%C3%A0_asociativa" title="Propietà asociativa – venetiansk" lang="vec" hreflang="vec" data-title="Propietà asociativa" data-language-autonym="Vèneto" data-language-local-name="venetiansk" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%C3%ADnh_k%E1%BA%BFt_h%E1%BB%A3p" title="Tính kết hợp – vietnamesisk" lang="vi" hreflang="vi" data-title="Tính kết hợp" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" 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/%E7%BB%93%E5%90%88%E5%BE%8B" title="结合律 – wu" lang="wuu" hreflang="wuu" data-title="结合律" 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-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%A1%D7%90%D7%A6%D7%99%D7%90%D7%98%D7%99%D7%95%D7%95%D7%99%D7%98%D7%A2%D7%98" title="אסאציאטיוויטעט – jiddisk" lang="yi" hreflang="yi" data-title="אסאציאטיוויטעט" data-language-autonym="ייִדיש" data-language-local-name="jiddisk" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%B5%90%E5%90%88%E5%BE%8B" title="結合律 – kantonesisk" lang="yue" hreflang="yue" data-title="結合律" data-language-autonym="粵語" data-language-local-name="kantonesisk" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%BB%93%E5%90%88%E5%BE%8B" title="结合律 – kinesisk" lang="zh" hreflang="zh" data-title="结合律" data-language-autonym="中文" data-language-local-name="kinesisk" class="interlanguage-link-target"><span>中文</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/Q177251#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Navnerom"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Assosiativ_lov" title="Vis innholdssiden [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskusjon:Assosiativ_lov&action=edit&redlink=1" rel="discussion" class="new" title="Diskusjon om innholdssiden (ikke skrevet ennå) [t]" accesskey="t"><span>Diskusjon</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" 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vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Assosiativ_lov&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Assosiativ_lov&action=history"><span>Vis historikk</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generelt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesial:Lenker_hit/Assosiativ_lov" title="Liste over alle wikisider som lenker hit [j]" accesskey="j"><span>Lenker hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesial:Relaterte_endringer/Assosiativ_lov" rel="nofollow" title="Siste endringer i sider som blir lenket fra denne siden [k]" accesskey="k"><span>Relaterte 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class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Fra Wikipedia, den frie encyklopedi</div> </div> <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="nb" dir="ltr"><p>En <b>assosiative lov</b> er i <a href="/wiki/Matematikk" title="Matematikk">matematikk</a> et <a href="/wiki/Teorem" title="Teorem">teorem</a> eller et <a href="/wiki/Aksiom" title="Aksiom">aksiom</a> sier at en <a href="/wiki/Bin%C3%A6r_operasjon" title="Binær operasjon">binær operasjon</a> er assosiativ.<sup id="cite_ref-EJBB1_1-0" class="reference"><a href="#cite_note-EJBB1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> En <b>assosiativ</b> operasjon tillater at <a href="/wiki/Parentes" title="Parentes">parenteser</a> kan plasseres fritt i et uttrykk der operasjonen utføres flere ganger i en sekvens. <a href="/wiki/Addisjon" title="Addisjon">Addisjon</a> av <a href="/wiki/Reelt_tall" title="Reelt tall">reelle tall</a> er et eksempel på en assosiativ operasjon, der ( 2 + 3 ) + 7 = 2 + ( 3 + 7 ). <a href="/wiki/Subtraksjon" title="Subtraksjon">Subtraksjon</a> er derimot ikke assosiativ, siden ( 7 - 2 ) - 3 ikke er lik 7 - ( 2 - 3 ). </p><p>Generelt vil parenteser bestemme rekkefølgen som ledd i en sammensatt operasjon skal utføres i. For å regne ut uttrykket </p> <dl><dd><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 (3+2)+(7+3)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>7</mn> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (3+2)+(7+3)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9afc39a9789bb2bf16d0a7d32f4a47a30f48ac8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.177ex; height:2.843ex;" alt="{\displaystyle (3+2)+(7+3)\,}"></span></dd></dl> <p>skal en først legge sammen (3 + 2), deretter (7 + 3) og så til slutt summere resultatene for de to parentesene. I sammensetninger av en assosiativ operasjon kan en utføre operasjonene i vilkårlig rekkefølge, så lenge rekkefølgen til leddene ikke endres. Endring av rekkefølgen er knyttet til egenskapen <a href="/wiki/Kommutativ_lov" title="Kommutativ lov">kommutativitet</a>, som ikke må forveksles med assosiativitet. </p><p>En <a href="/wiki/Algebraisk_struktur" title="Algebraisk struktur">algebraisk struktur</a> som inneholder en assosiativ operasjon kan omtales som en <i>assosiativ struktur</i>.<sup id="cite_ref-EJBB1_1-1" class="reference"><a href="#cite_note-EJBB1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Assosiativitet er en fundamental egenskap til mange operasjoner, og egenskapen blir ofte postulert i aksiomer som definerer operasjonen. Dette gjelder for eksempel for kroppsaksiomene for addisjon og <a href="/wiki/Multiplikasjon" title="Multiplikasjon">multiplikasjon</a> av reelle tall.<sup id="cite_ref-WR1_2-0" class="reference"><a href="#cite_note-WR1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Formell_definisjon">Formell definisjon</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Assosiativ_lov&veaction=edit&section=1" title="Rediger avsnitt: Formell definisjon" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Assosiativ_lov&action=edit&section=1" title="Rediger kildekoden til seksjonen Formell definisjon"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En binær operasjon <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/8e9972f426d9e07855984f73ee195a21dbc21755" 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 *}"></span> på en <a href="/wiki/Mengde" title="Mengde">mengde</a> <i>S</i> er <i>assosiativ</i> dersom </p> <dl><dd><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 (x*y)*z=x*(y*z)\qquad {\mbox{for all }}x,y,z\in S.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>∗</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∗</mo> <mi>z</mi> <mo>=</mo> <mi>x</mi> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>∗</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>for all </mtext> </mstyle> </mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>∈</mo> <mi>S</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x*y)*z=x*(y*z)\qquad {\mbox{for all }}x,y,z\in S.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c533f849868a9a80fe7be08a671a3638842a861b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.319ex; height:2.843ex;" alt="{\displaystyle (x*y)*z=x*(y*z)\qquad {\mbox{for all }}x,y,z\in S.}"></span></dd></dl> <p>Dersom en binære operasjonen uttrykkes som en funksjon <i>f(x,y)</i>, så vil operasjonen være assosiativ hvis og bare hvis funksjonen har egenskapen <i>f(f(x,y),z)</i> = <i>f(x,f(y,z))</i>. Operasjonen multiplikasjon kan for eksempel skrives som funksjonen <i>f(x,y) = xy</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Eksempler">Eksempler</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Assosiativ_lov&veaction=edit&section=2" title="Rediger avsnitt: Eksempler" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Assosiativ_lov&action=edit&section=2" title="Rediger kildekoden til seksjonen Eksempler"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Aritmetikk">Aritmetikk</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Assosiativ_lov&veaction=edit&section=3" title="Rediger avsnitt: Aritmetikk" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Assosiativ_lov&action=edit&section=3" title="Rediger kildekoden til seksjonen Aritmetikk"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Addisjon og multiplikasjon av reelle og <a href="/wiki/Komplekst_tall" title="Komplekst tall">komplekse tall</a> er assosiativ.</li></ul> <ul><li>Divisjon og <a href="/wiki/Subtraksjon" title="Subtraksjon">subtraksjon</a> er ikke assosiative operasjoner.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Matematikk_generelt">Matematikk generelt</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Assosiativ_lov&veaction=edit&section=4" title="Rediger avsnitt: Matematikk generelt" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Assosiativ_lov&action=edit&section=4" title="Rediger kildekoden til seksjonen Matematikk generelt"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Operasjonen å ta <a href="/wiki/Union_(mengdel%C3%A6re)" title="Union (mengdelære)">unionen</a> av to mengder er assosiativ. Det samme gjelder for <a href="/wiki/Snitt_(mengdel%C3%A6re)" title="Snitt (mengdelære)">snittet</a>:</li></ul> <dl><dd><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 \left.{\begin{matrix}(A\cap B)\cap C=A\cap (B\cap C)=A\cap B\cap C\quad \\(A\cup B)\cup C=A\cup (B\cup C)=A\cup B\cup C\quad \end{matrix}}\right\}{\mbox{for alle set }}A,B,C.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∩</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>∩</mo> <mi>C</mi> <mo>=</mo> <mi>A</mi> <mo>∩</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo>∩</mo> <mi>C</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mo>∩</mo> <mi>B</mi> <mo>∩</mo> <mi>C</mi> <mspace width="1em" /> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∪</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>∪</mo> <mi>C</mi> <mo>=</mo> <mi>A</mi> <mo>∪</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo>∪</mo> <mi>C</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mo>∪</mo> <mi>B</mi> <mo>∪</mo> <mi>C</mi> <mspace width="1em" /> </mtd> </mtr> </mtable> </mrow> <mo>}</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>for alle set </mtext> </mstyle> </mrow> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left.{\begin{matrix}(A\cap B)\cap C=A\cap (B\cap C)=A\cap B\cap C\quad \\(A\cup B)\cup C=A\cup (B\cup C)=A\cup B\cup C\quad \end{matrix}}\right\}{\mbox{for alle set }}A,B,C.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66dcc81fbbeb057bc8d3413916729c54c682dd18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:65.194ex; height:6.176ex;" alt="{\displaystyle \left.{\begin{matrix}(A\cap B)\cap C=A\cap (B\cap C)=A\cap B\cap C\quad \\(A\cup B)\cup C=A\cup (B\cup C)=A\cup B\cup C\quad \end{matrix}}\right\}{\mbox{for alle set }}A,B,C.}"></span></dd></dl> <ul><li><a href="/wiki/Kryssprodukt" class="mw-redirect" title="Kryssprodukt">Kryssproduktet</a> av to <a href="/wiki/Vektor_(matematikk)" title="Vektor (matematikk)">vektorer</a> i <b>R</b><sup>3</sup> er ikke assosiativt. Generelt vil</li></ul> <dl><dd><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 (\mathbf {u} \times \mathbf {v} )\times \mathbf {w} \neq \mathbf {u} \times (\mathbf {v} \times \mathbf {w} ),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo stretchy="false">)</mo> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>≠</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>×</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\mathbf {u} \times \mathbf {v} )\times \mathbf {w} \neq \mathbf {u} \times (\mathbf {v} \times \mathbf {w} ),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9260088709956ee010915faa25a69f81e22176ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.38ex; height:2.843ex;" alt="{\displaystyle (\mathbf {u} \times \mathbf {v} )\times \mathbf {w} \neq \mathbf {u} \times (\mathbf {v} \times \mathbf {w} ),}"></span></dd></dl> <p>når <b>u</b>, <b>v</b> og <b>w</b> er vektorer i <b>R</b><sup>3</sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Assosiativitet_i_matematiske_strukturer">Assosiativitet i matematiske strukturer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Assosiativ_lov&veaction=edit&section=5" title="Rediger avsnitt: Assosiativitet i matematiske strukturer" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Assosiativ_lov&action=edit&section=5" title="Rediger kildekoden til seksjonen Assosiativitet i matematiske strukturer"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Gruppeoperasjonen i en <a href="/wiki/Gruppe_(matematikk)" title="Gruppe (matematikk)">gruppe</a> er assosiativ.</li></ul> <ul><li>I en <a href="/wiki/Kropp_(matematikk)" class="mw-redirect" title="Kropp (matematikk)">kropp</a> er både addisjon og multiplikasjon assosiative. Det samme gjelder for en <a href="/wiki/Ring_(matematikk)" title="Ring (matematikk)">ring</a>.</li></ul> <ul><li>I en <a href="/wiki/Algebra" title="Algebra">algebra</a> er multiplikasjonen ikke nødvendigvis assosiativ.</li></ul> <ul><li>Vektoraddisjon i et <a href="/wiki/Vektorrom" title="Vektorrom">vektorrom</a> er assosiativ.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Se_også"><span id="Se_ogs.C3.A5"></span>Se også</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Assosiativ_lov&veaction=edit&section=6" title="Rediger avsnitt: Se også" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Assosiativ_lov&action=edit&section=6" title="Rediger kildekoden til seksjonen Se også"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Distributiv_lov" title="Distributiv lov">Distributiv lov</a></li> <li><a href="/wiki/Kommutativ_lov" title="Kommutativ lov">Kommutativ lov</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referanser">Referanser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Assosiativ_lov&veaction=edit&section=7" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Assosiativ_lov&action=edit&section=7" title="Rediger kildekoden til seksjonen Referanser"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-EJBB1-1"><b>^</b> <a href="#cite_ref-EJBB1_1-0"><sup>a</sup></a> <a href="#cite_ref-EJBB1_1-1"><sup>b</sup></a> <span class="reference-text"><a href="#EJBB">, E.J.Borowski, J.M.Borwein,1989</a>, <i>Associative</i>, s.35</span> </li> <li id="cite_note-WR1-2"><b><a href="#cite_ref-WR1_2-0">^</a></b> <span class="reference-text"><a href="#WR">W.Rudin, 1976</a>, s.5</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Litteratur">Litteratur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Assosiativ_lov&veaction=edit&section=8" title="Rediger avsnitt: Litteratur" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Assosiativ_lov&action=edit&section=8" title="Rediger kildekoden til seksjonen Litteratur"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="EJBB" class="citation book">E.J.Borowski, J.M.Borwein (1989). <i>Dictionary of mathematics</i>. Glasgow: Collins. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/0-00-434347-6" title="Spesial:Bokkilder/0-00-434347-6">0-00-434347-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AAssosiativ+lov&rft.au=E.J.Borowski%2C+J.M.Borwein&rft.btitle=Dictionary+of+mathematics&rft.date=1989&rft.genre=book&rft.isbn=0-00-434347-6&rft.place=Glasgow&rft.pub=Collins&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <ul><li><cite id="WR" class="citation book">Walter Rudin (1953). <i>Principles of mathematical analysis</i>. Singapore: McGraw-Hill International Book Co. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Spesial:Bokkilder/0-07-085613-3" title="Spesial:Bokkilder/0-07-085613-3">0-07-085613-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fno.wikipedia.org%3AAssosiativ+lov&rft.au=Walter+Rudin&rft.btitle=Principles+of+mathematical+analysis&rft.date=1953&rft.genre=book&rft.isbn=0-07-085613-3&rft.place=Singapore&rft.pub=McGraw-Hill+International+Book+Co.&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r23230704">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output 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