CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-disabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="af" dir="ltr"> <head> <meta charset="UTF-8"> <title>Kommutatiewe bewerking - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-disabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )afwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t."," \t,"],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","Januarie","Februarie","Maart","April","Mei","Junie","Julie","Augustus","September","Oktober","November","Desember"],"wgRequestId":"2fa39bc9-a331-4c10-a483-fd2552aea77b","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Kommutatiewe_bewerking","wgTitle":"Kommutatiewe bewerking","wgCurRevisionId":2578886,"wgRevisionId":2578886,"wgArticleId":15684,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Wiskunde"],"wgPageViewLanguage":"af","wgPageContentLanguage":"af","wgPageContentModel":"wikitext","wgRelevantPageName":"Kommutatiewe_bewerking","wgRelevantArticleId":15684,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"af","pageLanguageDir":"ltr","pageVariantFallbacks":"af"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":4000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q165474","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false}; RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["site","mediawiki.page.ready","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.charinsert","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=af&modules=ext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=af&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=af&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.20"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Kommutatiewe bewerking - Wikipedia"> <meta property="og:type" content="website"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//af.m.wikipedia.org/wiki/Kommutatiewe_bewerking"> <link rel="alternate" type="application/x-wiki" title="Wysig" href="/w/index.php?title=Kommutatiewe_bewerking&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (af)"> <link rel="EditURI" type="application/rsd+xml" href="//af.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://af.wikipedia.org/wiki/Kommutatiewe_bewerking"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.af"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atoomvoer" href="/w/index.php?title=Spesiaal:Onlangse_wysigings&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Kommutatiewe_bewerking rootpage-Kommutatiewe_bewerking skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Gaan na inhoud</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Werf"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Hoofkieslys" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Hoofkieslys" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Hoofkieslys</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Hoofkieslys</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">versteek</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigasie </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Tuisblad" title="Besoek die Tuisblad [z]" accesskey="z"><span>Tuisblad</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Gebruikersportaal" title="Meer oor die projek, wat jy kan doen, nuttige skakels"><span>Gebruikersportaal</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Wikipedia:Geselshoekie" title="Agtergrondinligting oor aktuele sake"><span>Geselshoekie</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spesiaal:Onlangse_wysigings" title="'n Lys van onlangse wysigings [r]" accesskey="r"><span>Onlangse wysigings</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesiaal:Lukraak" title="Laai 'n lukrake bladsye [x]" accesskey="x"><span>Lukrake bladsy</span></a></li><li id="n-help" class="mw-list-item"><a href="https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents" title="Vind meer uit oor iets"><span>Hulp</span></a></li><li id="n-Sandput" class="mw-list-item"><a href="/wiki/Wikipedia:Sandput"><span>Sandput</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Spesiaal:Spesiale_bladsye"><span>Spesiale bladsye</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Tuisblad" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-af.svg" width="118" height="13" style="width: 7.375em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Spesiaal:Soek" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Deursoek Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Soek</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Deursoek Wikipedia" aria-label="Deursoek Wikipedia" autocapitalize="sentences" title="Deursoek Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Spesiaal:Soek"> </div> <button class="cdx-button cdx-search-input__end-button">Soek</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Persoonlike gereedskap"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Voorkoms"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Voorkoms" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Voorkoms</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=af.wikipedia.org&uselang=af" class=""><span>Skenkings</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesiaal:SkepRekening&returnto=Kommutatiewe+bewerking" title="U word aangemoedig om 'n gebruiker te skep en aan te meld, hoewel dit nie verpligtend is nie." class=""><span>Skep gebruiker</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesiaal:Teken_in&returnto=Kommutatiewe+bewerking" title="U word aangemoedig om aan te meld. Dit is egter nie verpligtend nie. [o]" accesskey="o" class=""><span>Meld aan</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Meer opsies" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Persoonlike gereedskap" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Persoonlike gereedskap</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=af.wikipedia.org&uselang=af"><span>Skenkings</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesiaal:SkepRekening&returnto=Kommutatiewe+bewerking" title="U word aangemoedig om 'n gebruiker te skep en aan te meld, hoewel dit nie verpligtend is nie."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Skep gebruiker</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesiaal:Teken_in&returnto=Kommutatiewe+bewerking" title="U word aangemoedig om aan te meld. Dit is egter nie verpligtend nie. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Meld aan</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Bladsye vir uitgemelde redakteurs <a href="/wiki/Hulp:Inleiding" aria-label="Leer meer oor redigering"><span>leer meer</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Spesiaal:Mybydrae" title="A list of edits made from this IP address [y]" accesskey="y"><span>Bydraes</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spesiaal:Mybespreking" title="Bespreking oor bydraes van hierdie IP-adres [n]" accesskey="n"><span>Bespreking</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Werf"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Inhoud" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Inhoud</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">versteek</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">Inleiding</div> </a> </li> <li id="toc-Sien_ook" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sien_ook"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Sien ook</span> </div> </a> <ul id="toc-Sien_ook-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="Inhoud" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Inhoudsopgawe" > <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="Wissel die inhoudsopgawe" > <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">Wissel die inhoudsopgawe</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">Kommutatiewe bewerking</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="Gaan na 'n artikel in 'n ander taal. Beskikbaar in 70 tale" > <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-70" 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">70 tale</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D9%85%D9%84%D9%8A%D8%A9_%D8%AA%D8%A8%D8%AF%D9%8A%D9%84%D9%8A%D8%A9" title="عملية تبديلية – Arabies" lang="ar" hreflang="ar" data-title="عملية تبديلية" data-language-autonym="العربية" data-language-local-name="Arabies" 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/Conmutativid%C3%A1" title="Conmutatividá – Asturies" lang="ast" hreflang="ast" data-title="Conmutatividá" data-language-autonym="Asturianu" data-language-local-name="Asturies" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kommutativlik_xass%C9%99si" title="Kommutativlik xassəsi – Azerbeidjans" lang="az" hreflang="az" data-title="Kommutativlik xassəsi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidjans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BC%D1%83%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%D1%8B%D2%A1" title="Коммутативлыҡ – Baskir" lang="ba" hreflang="ba" data-title="Коммутативлыҡ" data-language-autonym="Башҡортса" data-language-local-name="Baskir" 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%9A%D0%B0%D0%BC%D1%83%D1%82%D0%B0%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="Камутатыўная аперацыя – Belarussies" lang="be" hreflang="be" data-title="Камутатыўная аперацыя" data-language-autonym="Беларуская" data-language-local-name="Belarussies" 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%9A%D0%BE%D0%BC%D1%83%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Комутативност – Bulgaars" lang="bg" hreflang="bg" data-title="Комутативност" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%A8%E0%A6%BF%E0%A6%AE%E0%A6%AF%E0%A6%BC_%E0%A6%AC%E0%A7%88%E0%A6%B6%E0%A6%BF%E0%A6%B7%E0%A7%8D%E0%A6%9F%E0%A7%8D%E0%A6%AF" title="বিনিময় বৈশিষ্ট্য – Bengaals" lang="bn" hreflang="bn" data-title="বিনিময় বৈশিষ্ট্য" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Komutativnost" title="Komutativnost – Bosnies" lang="bs" hreflang="bs" data-title="Komutativnost" data-language-autonym="Bosanski" data-language-local-name="Bosnies" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ca.wikipedia.org/wiki/Propietat_commutativa" title="Propietat commutativa – Katalaans" lang="ca" hreflang="ca" data-title="Propietat commutativa" data-language-autonym="Català" data-language-local-name="Katalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AE%D8%A7%D8%B3%DB%8C%DB%95%D8%AA%DB%8C_%D8%A6%D8%A7%DA%B5%D9%88%DA%AF%DB%86%DA%95" title="خاسیەتی ئاڵوگۆڕ – Sorani" lang="ckb" hreflang="ckb" data-title="خاسیەتی ئاڵوگۆڕ" data-language-autonym="کوردی" data-language-local-name="Sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Komutativita" title="Komutativita – Tsjeggies" lang="cs" hreflang="cs" data-title="Komutativita" data-language-autonym="Čeština" data-language-local-name="Tsjeggies" 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%9A%D0%BE%D0%BC%D0%BC%D1%83%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%C4%83_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8" title="Коммутативлă операци – Chuvash" lang="cv" hreflang="cv" data-title="Коммутативлă операци" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kommutativitet" title="Kommutativitet – Deens" lang="da" hreflang="da" data-title="Kommutativitet" data-language-autonym="Dansk" data-language-local-name="Deens" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kommutativgesetz" title="Kommutativgesetz – Duits" lang="de" hreflang="de" data-title="Kommutativgesetz" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BD%CF%84%CE%B9%CE%BC%CE%B5%CF%84%CE%B1%CE%B8%CE%B5%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="Αντιμεταθετική ιδιότητα – Grieks" lang="el" hreflang="el" data-title="Αντιμεταθετική ιδιότητα" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://en.wikipedia.org/wiki/Commutative_property" title="Commutative property – Engels" lang="en" hreflang="en" data-title="Commutative property" data-language-autonym="English" data-language-local-name="Engels" 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/Komuteco" title="Komuteco – Esperanto" lang="eo" hreflang="eo" data-title="Komuteco" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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/Conmutatividad" title="Conmutatividad – Spaans" lang="es" hreflang="es" data-title="Conmutatividad" data-language-autonym="Español" data-language-local-name="Spaans" 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/Kommutatiivsus" title="Kommutatiivsus – Estnies" lang="et" hreflang="et" data-title="Kommutatiivsus" data-language-autonym="Eesti" data-language-local-name="Estnies" 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/Trukakortasun" title="Trukakortasun – Baskies" lang="eu" hreflang="eu" data-title="Trukakortasun" data-language-autonym="Euskara" data-language-local-name="Baskies" 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%AC%D8%A7%D8%A8%D9%87%E2%80%8C%D8%AC%D8%A7%DB%8C%DB%8C" title="خاصیت جابه‌جایی – Persies" lang="fa" hreflang="fa" data-title="خاصیت جابه‌جایی" data-language-autonym="فارسی" data-language-local-name="Persies" 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/Vaihdannaisuus" title="Vaihdannaisuus – Fins" lang="fi" hreflang="fi" data-title="Vaihdannaisuus" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Loi_commutative" title="Loi commutative – Frans" lang="fr" hreflang="fr" data-title="Loi commutative" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Komutatiifgesets" title="Komutatiifgesets – Noord-Fries" lang="frr" hreflang="frr" data-title="Komutatiifgesets" data-language-autonym="Nordfriisk" data-language-local-name="Noord-Fries" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Oibr%C3%ADocht_ch%C3%B3mhalartach" title="Oibríocht chómhalartach – Iers" lang="ga" hreflang="ga" data-title="Oibríocht chómhalartach" data-language-autonym="Gaeilge" data-language-local-name="Iers" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Co-iomlaideachd" title="Co-iomlaideachd – Skotse Gallies" lang="gd" hreflang="gd" data-title="Co-iomlaideachd" data-language-autonym="Gàidhlig" data-language-local-name="Skotse Gallies" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Conmutatividade" title="Conmutatividade – Galisies" lang="gl" hreflang="gl" data-title="Conmutatividade" data-language-autonym="Galego" data-language-local-name="Galisies" 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%A4%D7%A2%D7%95%D7%9C%D7%94_%D7%A7%D7%95%D7%9E%D7%95%D7%98%D7%98%D7%99%D7%91%D7%99%D7%AA" title="פעולה קומוטטיבית – Hebreeus" lang="he" hreflang="he" data-title="פעולה קומוטטיבית" data-language-autonym="עברית" data-language-local-name="Hebreeus" 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%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%B5%E0%A4%BF%E0%A4%A8%E0%A4%BF%E0%A4%AE%E0%A5%87%E0%A4%AF%E0%A4%A4%E0%A4%BE" title="क्रमविनिमेयता – Hindi" lang="hi" hreflang="hi" data-title="क्रमविनिमेयता" 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/Komutativnost" title="Komutativnost – Kroaties" lang="hr" hreflang="hr" data-title="Komutativnost" data-language-autonym="Hrvatski" data-language-local-name="Kroaties" 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/Kommutativit%C3%A1s" title="Kommutativitás – Hongaars" lang="hu" hreflang="hu" data-title="Kommutativitás" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%A5%D5%B2%D5%A1%D6%83%D5%B8%D5%AD%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Տեղափոխականություն – Armeens" lang="hy" hreflang="hy" data-title="Տեղափոխականություն" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Commutativitate" title="Commutativitate – Interlingua" lang="ia" hreflang="ia" data-title="Commutativitate" 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/Sifat_komutatif" title="Sifat komutatif – Indonesies" lang="id" hreflang="id" data-title="Sifat komutatif" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesies" 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/V%C3%ADxlregla" title="Víxlregla – Yslands" lang="is" hreflang="is" data-title="Víxlregla" data-language-autonym="Íslenska" data-language-local-name="Yslands" 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/Commutativit%C3%A0" title="Commutatività – Italiaans" lang="it" hreflang="it" data-title="Commutatività" data-language-autonym="Italiano" data-language-local-name="Italiaans" 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/%E4%BA%A4%E6%8F%9B%E6%B3%95%E5%89%87" title="交換法則 – Japannees" lang="ja" hreflang="ja" data-title="交換法則" data-language-autonym="日本語" data-language-local-name="Japannees" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%83%D1%8B%D1%81%D1%82%D1%8B%D1%80%D1%8B%D0%BC%D0%B4%D1%8B%D0%BB%D1%8B%D2%9B" title="Ауыстырымдылық – Kazaks" lang="kk" hreflang="kk" data-title="Ауыстырымдылық" data-language-autonym="Қазақша" data-language-local-name="Kazaks" 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%ED%99%98%EB%B2%95%EC%B9%99" title="교환법칙 – Koreaans" lang="ko" hreflang="ko" data-title="교환법칙" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Commutativitas_(mathematica)" title="Commutativitas (mathematica) – Latyn" lang="la" hreflang="la" data-title="Commutativitas (mathematica)" data-language-autonym="Latina" data-language-local-name="Latyn" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Komutatyvumas" title="Komutatyvumas – Litaus" lang="lt" hreflang="lt" data-title="Komutatyvumas" data-language-autonym="Lietuvių" data-language-local-name="Litaus" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Komutativit%C4%81te" title="Komutativitāte – Letties" lang="lv" hreflang="lv" data-title="Komutativitāte" data-language-autonym="Latviešu" data-language-local-name="Letties" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D1%83%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Комутативност – Masedonies" lang="mk" hreflang="mk" data-title="Комутативност" data-language-autonym="Македонски" data-language-local-name="Masedonies" 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%95%E0%B5%8D%E0%B4%B0%E0%B4%AE%E0%B4%A8%E0%B4%BF%E0%B4%AF%E0%B4%AE%E0%B4%82" title="ക്രമനിയമം – Malabaars" lang="ml" hreflang="ml" data-title="ക്രമനിയമം" data-language-autonym="മലയാളം" data-language-local-name="Malabaars" 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_tukar_tertib" title="Kalis tukar tertib – Maleis" lang="ms" hreflang="ms" data-title="Kalis tukar tertib" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" 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/Commutativiteit" title="Commutativiteit – Nederlands" lang="nl" hreflang="nl" data-title="Commutativiteit" data-language-autonym="Nederlands" data-language-local-name="Nederlands" 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/Kommutativitet" title="Kommutativitet – Nuwe Noors" lang="nn" hreflang="nn" data-title="Kommutativitet" data-language-autonym="Norsk nynorsk" data-language-local-name="Nuwe Noors" 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/Kommutativ_lov" title="Kommutativ lov – Boeknoors" lang="nb" hreflang="nb" data-title="Kommutativ lov" data-language-autonym="Norsk bokmål" data-language-local-name="Boeknoors" 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/Przemienno%C5%9B%C4%87" title="Przemienność – Pools" lang="pl" hreflang="pl" data-title="Przemienność" data-language-autonym="Polski" data-language-local-name="Pools" 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/Comutatividade" title="Comutatividade – Portugees" lang="pt" hreflang="pt" data-title="Comutatividade" data-language-autonym="Português" data-language-local-name="Portugees" 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/Comutativitate" title="Comutativitate – Roemeens" lang="ro" hreflang="ro" data-title="Comutativitate" data-language-autonym="Română" data-language-local-name="Roemeens" 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%9A%D0%BE%D0%BC%D0%BC%D1%83%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Коммутативность – Russies" lang="ru" hreflang="ru" data-title="Коммутативность" data-language-autonym="Русский" data-language-local-name="Russies" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Komutativnost" title="Komutativnost – Serwo-Kroaties" lang="sh" hreflang="sh" data-title="Komutativnost" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serwo-Kroaties" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B1%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%AF%E0%B7%9A%E0%B7%81%E0%B7%8A%E2%80%8D%E0%B6%BA_%E0%B6%B1%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%BA" title="න්‍යාදේශ්‍ය න්‍යාය – Sinhala" lang="si" hreflang="si" data-title="න්‍යාදේශ්‍ය න්‍යාය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Commutative_property" title="Commutative property – Simple English" lang="en-simple" hreflang="en-simple" data-title="Commutative property" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Komutat%C3%ADvnos%C5%A5" title="Komutatívnosť – Slowaaks" lang="sk" hreflang="sk" data-title="Komutatívnosť" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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/Komutativnost" title="Komutativnost – Sloweens" lang="sl" hreflang="sl" data-title="Komutativnost" data-language-autonym="Slovenščina" data-language-local-name="Sloweens" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Vetia_e_nd%C3%ABrrimit" title="Vetia e ndërrimit – Albanees" lang="sq" hreflang="sq" data-title="Vetia e ndërrimit" data-language-autonym="Shqip" data-language-local-name="Albanees" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D1%83%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Комутативност – Serwies" lang="sr" hreflang="sr" data-title="Комутативност" data-language-autonym="Српски / srpski" data-language-local-name="Serwies" 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/Kommutativitet" title="Kommutativitet – Sweeds" lang="sv" hreflang="sv" data-title="Kommutativitet" data-language-autonym="Svenska" data-language-local-name="Sweeds" 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%AA%E0%AE%B0%E0%AE%BF%E0%AE%AE%E0%AE%BE%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AF%81%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%A9%E0%AF%8D%E0%AE%AE%E0%AF%88" title="பரிமாற்றுத்தன்மை – Tamil" lang="ta" hreflang="ta" data-title="பரிமாற்றுத்தன்மை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" 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%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%B8%AA%E0%B8%A5%E0%B8%B1%E0%B8%9A%E0%B8%97%E0%B8%B5%E0%B9%88" title="สมบัติการสลับที่ – Thai" lang="th" hreflang="th" data-title="สมบัติการสลับที่" 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/De%C4%9Fi%C5%9Fme_%C3%B6zelli%C4%9Fi" title="Değişme özelliği – Turks" lang="tr" hreflang="tr" data-title="Değişme özelliği" data-language-autonym="Türkçe" data-language-local-name="Turks" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BC%D1%83%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%D1%8B%D0%BA" title="Коммутативлык – Tataars" lang="tt" hreflang="tt" data-title="Коммутативлык" data-language-autonym="Татарча / tatarça" data-language-local-name="Tataars" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D1%83%D1%82%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Комутативність – Oekraïens" lang="uk" hreflang="uk" data-title="Комутативність" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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_comutativa" title="Propietà comutativa – Venesiaans" lang="vec" hreflang="vec" data-title="Propietà comutativa" data-language-autonym="Vèneto" data-language-local-name="Venesiaans" 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_giao_ho%C3%A1n" title="Tính giao hoán – Viëtnamees" lang="vi" hreflang="vi" data-title="Tính giao hoán" data-language-autonym="Tiếng Việt" data-language-local-name="Viëtnamees" 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%E6%8D%A2%E5%BE%8B" title="交换律 – Wu-Sjinees" lang="wuu" hreflang="wuu" data-title="交换律" data-language-autonym="吴语" data-language-local-name="Wu-Sjinees" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%A4%E6%8F%9B%E5%BE%8B" title="交換律 – Chinees" lang="zh" hreflang="zh" data-title="交換律" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BA%A4%E6%8F%9B%E5%BE%8B" title="交換律 – Kantonees" lang="yue" hreflang="yue" data-title="交換律" data-language-autonym="粵語" data-language-local-name="Kantonees" 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/Q165474#sitelinks-wikipedia" title="Wysig skakels tussen tale" class="wbc-editpage">Wysig skakels</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="Naamruimtes"> <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/Kommutatiewe_bewerking" title="Bekyk die inhoudbladsy [c]" accesskey="c"><span>Bladsy</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Bespreking:Kommutatiewe_bewerking" rel="discussion" title="Bespreking oor die inhoudbladsy [t]" accesskey="t"><span>Bespreking</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Verander taalvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Afrikaans</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Weergawes"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Kommutatiewe_bewerking"><span>Lees</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&veaction=edit" title="Redigeer hierdie bladsy [v]" accesskey="v"><span>Wysig</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&action=edit" title="Wysig die bladsy se bonkode [e]" accesskey="e"><span>Wysig bron</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&action=history" title="Ouer weergawes van hierdie bladsy [h]" accesskey="h"><span>Wys geskiedenis</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Gereedskap" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Gereedskap</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Gereedskap</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">versteek</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Kommutatiewe_bewerking"><span>Lees</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&veaction=edit" title="Redigeer hierdie bladsy [v]" accesskey="v"><span>Wysig</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&action=edit" title="Wysig die bladsy se bonkode [e]" accesskey="e"><span>Wysig bron</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&action=history"><span>Wys geskiedenis</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Algemeen </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesiaal:Skakels_hierheen/Kommutatiewe_bewerking" title="'n Lys bladsye wat hierheen skakel [j]" accesskey="j"><span>Skakels hierheen</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesiaal:OnlangseVeranderingsMetSkakels/Kommutatiewe_bewerking" rel="nofollow" title="Onlangse wysigings aan bladsye wat vanaf hierdie bladsy geskakel is [k]" accesskey="k"><span>Verwante veranderings</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&oldid=2578886" title="'n Permanente skakel na hierdie weergawe van die bladsy"><span>Permanente skakel</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&action=info" title="More information about this page"><span>Bladinligting</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:CiteThisPage&page=Kommutatiewe_bewerking&id=2578886&wpFormIdentifier=titleform" title="Inligting oor hoe u hierdie bladsy kan verwys"><span>Haal dié blad aan</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:UrlShortener&url=https%3A%2F%2Faf.wikipedia.org%2Fwiki%2FKommutatiewe_bewerking"><span>Kry verkorte URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:QrCode&url=https%3A%2F%2Faf.wikipedia.org%2Fwiki%2FKommutatiewe_bewerking"><span>Laai QR-kode af</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Druk/uitvoer </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:Boek&bookcmd=book_creator&referer=Kommutatiewe+bewerking"><span>Skep boek</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Spesiaal:DownloadAsPdf&page=Kommutatiewe_bewerking&action=show-download-screen"><span>Laai af as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Kommutatiewe_bewerking&printable=yes" title="Drukbare weergawe van hierdie bladsy [p]" accesskey="p"><span>Drukbare weergawe</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Ander projekte </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Commutativity" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q165474" title="Skakel na gekonnekteerde databank item [g]" accesskey="g"><span>Wikidata-item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Voorkoms"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Voorkoms</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">versteek</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">in Wikipedia, die vrye ensiklopedie</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="af" dir="ltr"><p>'n Funksie of binêre bewerking <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:A\times B\rightarrow C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>A</mi> <mo>×</mo> <mi>B</mi> <mo stretchy="false">→</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:A\times B\rightarrow C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b88043b27b007276d47ed82698fa6cd11f5f5d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.944ex; height:2.509ex;" alt="{\displaystyle f:A\times B\rightarrow C}" /></span> word <b>kommutatief</b> genoem wanneer daar vir enige <i>y</i> in <i>A</i> en enige <i>z</i> in <i>B</i> geld dat<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 f(y,z)=f(z,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(y,z)=f(z,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc6562be7b57a0bb7d6991dc75460fd5c7e0c700" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.829ex; height:2.843ex;" alt="{\displaystyle f(y,z)=f(z,y)}" /></span>; anders word die bewerking <b>nie-kommutatief</b> genoem. </p><p>Die vermenigvuldiging van reële getalle is kommutatief aangesien </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 yz=zy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mi>z</mi> <mo>=</mo> <mi>z</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle yz=zy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5d0b84cbffcb9655310034e84e5985b9d2cdd7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.586ex; height:2.009ex;" alt="{\displaystyle yz=zy}" /></span></dd></dl> <p>vir <i>alle</i> <a href="/wiki/Re%C3%ABle_getal" title="Reële getal">reële getalle</a> <i>y</i> en <i>z</i>. Aan die ander kant, is die aftrekking van reële getalle nie-kommutatief nie, aangesien </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 y-z=z-y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>−</mo> <mi>z</mi> <mo>=</mo> <mi>z</mi> <mo>−</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y-z=z-y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2157743026cbed3a62bac3834609d744f7b8b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.266ex; height:2.343ex;" alt="{\displaystyle y-z=z-y}" /></span></dd></dl> <p><a href="/w/index.php?title=As_en_slegs_as&action=edit&redlink=1" class="new" title="As en slegs as (bladsy bestaan nie)">as en slegs as</a> <i>y</i> en <i>z</i> identies is. </p><p>Verder as </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 f(y,z)=f(z,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(y,z)=f(z,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc6562be7b57a0bb7d6991dc75460fd5c7e0c700" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.829ex; height:2.843ex;" alt="{\displaystyle f(y,z)=f(z,y)}" /></span></dd></dl> <p>vir 'n <i>spesifieke</i> paar elmente <i>y</i> en <i>z</i>, dan word gesê dat <i>y</i> en <i>z</i>, kommuteer. Elke element kommuteer met homself en in 'n <a href="/wiki/Groep_(wiskunde)" title="Groep (wiskunde)">groep</a> kommuteer elke element met die <a href="/w/index.php?title=Identiteit_(wiskunde)&action=edit&redlink=1" class="new" title="Identiteit (wiskunde) (bladsy bestaan nie)">identiteit</a>, met sy eie <a href="/w/index.php?title=Inverse&action=edit&redlink=1" class="new" title="Inverse (bladsy bestaan nie)">inverse</a> en met sy <a href="/wiki/Eksponent" title="Eksponent">eksponent</a>. </p><p>Die bekendste voorbeelde van kommutatiewe binêre bewerkings is <a href="/w/index.php?title=Sommering&action=edit&redlink=1" class="new" title="Sommering (bladsy bestaan nie)">sommering</a> en <a href="/wiki/Vermenigvuldiging" title="Vermenigvuldiging">vermenigvuldiging</a> van <a href="/wiki/Re%C3%ABle_getal" title="Reële getal">reële getalle</a>; byvoorbeeld: </p> <ul><li>4 + 5 = 5 + 4 (aangesien beide <a href="/w/index.php?title=Vergelyking_(mathematics)&action=edit&redlink=1" class="new" title="Vergelyking (mathematics) (bladsy bestaan nie)">vergelykings</a> die resultaat 9 lewer)</li> <li>2 × 3 = 3 × 2 (aangesien beidie vergelykings die resultaat van 6 lewer)</li></ul> <p>Verdere voorbeelde van kommutatiewe binêre bewerkings sluit sommering en vermenigvuldiging van <a href="/wiki/Komplekse_getal" title="Komplekse getal">komplekse getalle</a>, sommering van <a href="/w/index.php?title=Vektor-ruimte&action=edit&redlink=1" class="new" title="Vektor-ruimte (bladsy bestaan nie)">vektore</a> en die <a href="/w/index.php?title=Snyding_(versameliingsteorie)&action=edit&redlink=1" class="new" title="Snyding (versameliingsteorie) (bladsy bestaan nie)">snyding</a>- en <a href="/w/index.php?title=Vereniging_(versamelingsteorie)&action=edit&redlink=1" class="new" title="Vereniging (versamelingsteorie) (bladsy bestaan nie)">vereniging</a> van <a href="/wiki/Versameling" title="Versameling">versamelings</a>. In elke geval is hierdie bewerkinge kommutatief oor die getaldomein in sy geheel. </p><p>Die nie-kommutatiewe binêre bewerkings is <a href="/w/index.php?title=Aftrekking&action=edit&redlink=1" class="new" title="Aftrekking (bladsy bestaan nie)">aftrekking</a> (<i>a</i> − <i>b</i>), <a href="/wiki/Deling" title="Deling">deling</a> (<i>a</i>/<i>b</i>), <a href="/wiki/Magsverheffing" title="Magsverheffing">magsverheffing</a> (<i>a</i><sup><i>b</i></sup>), <a href="/w/index.php?title=Funksiesamestelling&action=edit&redlink=1" class="new" title="Funksiesamestelling (bladsy bestaan nie)">funksiesamestelling</a> (<i>f</i> <small>o</small> <i>g</i>), <a href="/w/index.php?title=Tetrasie&action=edit&redlink=1" class="new" title="Tetrasie (bladsy bestaan nie)">tetrasie</a> (<i>a</i> ↑↑<i>b</i>), <a href="/wiki/Matriks_(wiskunde)" class="mw-redirect" title="Matriks (wiskunde)">matriksvermenigvuldiging</a> en <a href="/w/index.php?title=Kwartern%C3%AAre&action=edit&redlink=1" class="new" title="Kwarternêre (bladsy bestaan nie)">kwarternêre</a> vermenigvuldiging. </p><p>'n Baie goeie voorbeeld van nie-kommutatiwiteit uit die alledaagse lewe is die <a href="/w/index.php?title=Rubik%27s_Cube&action=edit&redlink=1" class="new" title="Rubik's Cube (bladsy bestaan nie)">Rubik's Cube</a>: dier byvoorbeeld die voorste vlak kloksgewys te draai, die boonste vlak kloksgewys te draai en die voorste vlak antikloksgewys te draai lewer nie dieselfde resultaat wanneer die volgorde van die aksies omgeruil word nie. Hierdie is tipies 'n verskynsel wat in <a href="/w/index.php?title=Groepteorie&action=edit&redlink=1" class="new" title="Groepteorie (bladsy bestaan nie)">groepteorie</a> bestudeer word. </p><p>Die onderstel van die domein waarop 'n bewerking kommutatief uitgevoer kan word, word soms die <a href="/w/index.php?title=Middel_(algebra)&action=edit&redlink=1" class="new" title="Middel (algebra) (bladsy bestaan nie)">middel</a> in <a href="/wiki/Algebra" title="Algebra">algebra</a> genoem. </p><p>'n <a href="/w/index.php?title=Abeliese_groep&action=edit&redlink=1" class="new" title="Abeliese groep (bladsy bestaan nie)">Abeliese groep</a> is 'n <a href="/wiki/Groep_(wiskunde)" title="Groep (wiskunde)">groep</a> waarvan die groepsbewerkinge kommutatief is. 'n <a href="/w/index.php?title=Kommutatiewe_ring&action=edit&redlink=1" class="new" title="Kommutatiewe ring (bladsy bestaan nie)">Kommutatiewe ring</a> is 'n <a href="/w/index.php?title=Ring_(wiskunde)&action=edit&redlink=1" class="new" title="Ring (wiskunde) (bladsy bestaan nie)">ring</a> waarvan die <a href="/wiki/Vermenigvuldiging" title="Vermenigvuldiging">vermenigvuldiging</a> kommutatief is (Sommering in 'n ring is altyd kommutatief). In 'n <a href="/w/index.php?title=Veld_(wiskunde)&action=edit&redlink=1" class="new" title="Veld (wiskunde) (bladsy bestaan nie)">veld</a> is beide sommering en vermenigvuldiging kommutatief. </p><p>Kommutatiwiteit kan ook 'n ander naam wees vir simmetrie. Met ander woorde veronderstel ons los 'n probleem op wat die parameters <i>x</i> en <i>y</i> bevat en bepaal dan dat daardie oplossing gelykstaande is aan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29473ed0c4e838ac9dbe074535e507166c0e9101" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.607ex; height:2.843ex;" alt="{\displaystyle f(x,y)}" /></span>. As daar 'n onderstel van waardes vir <i>x</i> en <i>y</i> bestaan waar die twee waardes uitgeruil kan word sonder om die funksie te beïnvloed, dan is die probleem <a href="/wiki/Simmetrie" title="Simmetrie">simmetries</a>. Simmetrie vloei normaalweg in wiskunde uit vanaf eenvoudiger simmetrie en word dikwels gebruik vir verskeie soorte bewyse. </p> <div class="mw-heading mw-heading2"><h2 id="Sien_ook">Sien ook</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kommutatiewe_bewerking&veaction=edit&section=1" title="Wysig afdeling: Sien ook" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kommutatiewe_bewerking&action=edit&section=1" title="Edit section's source code: Sien ook"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Antikommutatiwiteit&action=edit&redlink=1" class="new" title="Antikommutatiwiteit (bladsy bestaan nie)">Antikommutatiwiteit</a></li> <li><a href="/w/index.php?title=Assosiatiwiteit&action=edit&redlink=1" class="new" title="Assosiatiwiteit (bladsy bestaan nie)">Assosiatiwiteit</a></li> <li><a href="/w/index.php?title=Distribuwiteit&action=edit&redlink=1" class="new" title="Distribuwiteit (bladsy bestaan nie)">Distribuwiteit</a></li> <li><a href="/wiki/Eienskappe_van_bin%C3%AAre_bewerkings" title="Eienskappe van binêre bewerkings">Eienskappe van binêre bewerkings</a></li> <li><a href="/w/index.php?title=Kommutant&action=edit&redlink=1" class="new" title="Kommutant (bladsy bestaan nie)">Kommutant</a></li> <li><a href="/w/index.php?title=Kommutatief_(neurofisiologie)&action=edit&redlink=1" class="new" title="Kommutatief (neurofisiologie) (bladsy bestaan nie)">Kommutatief (neurofisiologie)</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Ontsluit van "<a dir="ltr" href="https://af.wikipedia.org/w/index.php?title=Kommutatiewe_bewerking&oldid=2578886">https://af.wikipedia.org/w/index.php?title=Kommutatiewe_bewerking&oldid=2578886</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Spesiaal:Kategorie%C3%AB" title="Spesiaal:Kategorieë">Kategorie</a>: <ul><li><a href="/wiki/Kategorie:Wiskunde" title="Kategorie:Wiskunde">Wiskunde</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Die bladsy is laas op 6 Junie 2023 om 14:43 bygewerk.</li> <li id="footer-info-copyright">Die teks is beskikbaar onder die lisensie <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Erkenning-Insgelyks Deel</a>. Aanvullende voorwaardes kan moontlik ook van toepassing wees. Sien die <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">Algemene Voorwaardes</a> vir meer inligting.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privaatheidsbeleid</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:Oor">Inligting oor Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Voorwaardes">Vrywaring</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Gedragskode</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Ontwikkelaars</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/af.wikipedia.org">Statistieke</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Koekieverklaring</a></li> <li id="footer-places-mobileview"><a href="//af.m.wikipedia.org/w/index.php?title=Kommutatiewe_bewerking&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Selfoonweergawe</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/static/images/footer/wikimedia-button.svg" width="84" height="29"><img src="/static/images/footer/wikimedia.svg" width="25" height="25" alt="Wikimedia Foundation" lang="en" loading="lazy"></picture></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/w/resources/assets/poweredby_mediawiki.svg" width="88" height="31"><img src="/w/resources/assets/mediawiki_compact.svg" alt="Powered by MediaWiki" lang="en" width="25" height="25" loading="lazy"></picture></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Soek</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Deursoek Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Spesiaal:Soek"> </div> <button class="cdx-button cdx-search-input__end-button">Soek</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Inhoud" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Wissel die inhoudsopgawe" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-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">Wissel die inhoudsopgawe</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Kommutatiewe bewerking</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>70 tale</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Nuwe onderwerp</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> <script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-56f98d4d58-r5cgr","wgBackendResponseTime":139,"wgPageParseReport":{"limitreport":{"cputime":"0.048","walltime":"0.178","ppvisitednodes":{"value":85,"limit":1000000},"postexpandincludesize":{"value":0,"limit":2097152},"templateargumentsize":{"value":0,"limit":2097152},"expansiondepth":{"value":5,"limit":100},"expensivefunctioncount":{"value":1,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":216,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 43.004 1 Sjabloon:Normdata","100.00% 43.004 1 -total"]},"scribunto":{"limitreport-timeusage":{"value":"0.017","limit":"10.000"},"limitreport-memusage":{"value":825586,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-958d75f5c-7vvng","timestamp":"20250306011444","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Kommutatiewe bewerking","url":"https:\/\/af.wikipedia.org\/wiki\/Kommutatiewe_bewerking","sameAs":"http:\/\/www.wikidata.org\/entity\/Q165474","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q165474","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2006-08-03T11:27:02Z","dateModified":"2023-06-06T14:43:03Z"}</script> </body> </html>