CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-enabled skin-theme-clientpref-day vector-toc-available" lang="nb" dir="ltr"> <head> <meta charset="UTF-8"> <title>Binær operasjon – Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )nowikimwclientpreferences=([^;]+)/);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":["","januar","februar","mars","april","mai","juni","juli","august","september","oktober","november","desember"],"wgRequestId":"d143881c-cf3b-4fb5-8e87-f6085a5b73da","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Binær_operasjon","wgTitle":"Binær operasjon","wgCurRevisionId":15669615,"wgRevisionId":15669615,"wgArticleId":2992,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Artikler med autoritetsdatalenker fra Wikidata","Algebra","Binære operasjoner"],"wgPageViewLanguage":"nb","wgPageContentLanguage":"nb","wgPageContentModel":"wikitext","wgRelevantPageName":"Binær_operasjon","wgRelevantArticleId":2992,"wgTempUserName":null,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick": true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"nb","pageLanguageDir":"ltr","pageVariantFallbacks":"nb"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":5000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q164307","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.InterProjectLinks":"ready","ext.globalCssJs.user.styles":"ready","site.styles" :"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","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=["ext.cite.ux-enhancements","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.UkensKonkurranse","ext.gadget.link-missing-label","ext.gadget.new-section","ext.gadget.superinterwiki","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","oojs-ui.styles.icons-media","oojs-ui-core.icons","wikibase.sidebar.tracking"];</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=nb&modules=ext.cite.styles%7Cext.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=nb&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=nb&modules=ext.gadget.InterProjectLinks&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=nb&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <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="Binær operasjon – Wikipedia"> <meta property="og:type" content="website"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//no.m.wikipedia.org/wiki/Bin%C3%A6r_operasjon"> <link rel="alternate" type="application/x-wiki" title="Rediger" href="/w/index.php?title=Bin%C3%A6r_operasjon&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 (nb)"> <link rel="EditURI" type="application/rsd+xml" href="//no.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://no.wikipedia.org/wiki/Bin%C3%A6r_operasjon"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.no"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom-mating" href="/w/index.php?title=Spesial:Siste_endringer&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-Binær_operasjon rootpage-Binær_operasjon skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Hopp til innhold</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="Nettsted"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <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="Hovedmeny" > <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">Hovedmeny</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">Hovedmeny</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">skjul</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigasjon </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Forside" title="Gå til hovedsiden [z]" accesskey="z"><span>Forside</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesial:Tilfeldig" title="Vis en tilfeldig side [x]" accesskey="x"><span>Tilfeldig side</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Hjelp:Portal" title="Stedet for å få hjelp"><span>Hjelp</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spesial:Siste_endringer" title="Liste over siste endringer på wikien. [r]" accesskey="r"><span>Siste endringer</span></a></li> </ul> </div> </div> <div id="p-prosjekt" class="vector-menu mw-portlet mw-portlet-prosjekt" > <div class="vector-menu-heading"> Prosjekt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Prosjektportal" class="mw-list-item"><a href="/wiki/Wikipedia:Portal"><span>Prosjektportal</span></a></li><li id="n-bidra" class="mw-list-item"><a href="/wiki/Wikipedia:Bidra_til_Wikipedia"><span>Hvordan bidra?</span></a></li><li id="n-tinget" class="mw-list-item"><a href="/wiki/Wikipedia:Tinget"><span>Tinget</span></a></li><li id="n-torget" class="mw-list-item"><a href="/wiki/Wikipedia:Torget"><span>Torget</span></a></li><li id="n-konkurranser" class="mw-list-item"><a href="/wiki/Wikipedia:Konkurranser"><span>Konkurranser</span></a></li> </ul> </div> </div> <div id="p-Wikipedia" class="vector-menu mw-portlet mw-portlet-Wikipedia" > <div class="vector-menu-heading"> Wikipedia </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-kontakt" class="mw-list-item"><a href="/wiki/Wikipedia:Kontakt"><span>Kontakt Wikipedia</span></a></li><li id="n-wmno" class="mw-list-item"><a href="https://www.wikimedia.no" rel="nofollow" title="Medlemsorganisasjon for wikipedianere"><span>Wikimedia Norge</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Forside" 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-no.svg" width="121" height="14" style="width: 7.5625em; height: 0.875em;"> </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/Spesial:S%C3%B8k" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Søk i Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Søk</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="Søk i Wikipedia" aria-label="Søk i Wikipedia" autocapitalize="sentences" title="Søk i 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="Spesial:Søk"> </div> <button class="cdx-button cdx-search-input__end-button">Søk</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personlig"> <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="Utseende"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Endre skriftstørrelse, bredde og farge på siden." > <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="Utseende" > <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">Utseende</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="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb" class=""><span>Doner</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=Spesial:Opprett_konto&returnto=Bin%C3%A6r+operasjon" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk" class=""><span>Opprett konto</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=Spesial:Logg_inn&returnto=Bin%C3%A6r+operasjon" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o" class=""><span>Logg inn</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 user-links-collapsible-item" title="Flere alternativer" > <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="Personlig" > <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">Personlig</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Brukermeny" > <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="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb"><span>Doner</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Opprett_konto&returnto=Bin%C3%A6r+operasjon" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Opprett konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Logg_inn&returnto=Bin%C3%A6r+operasjon" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logg inn</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="Nettsted"> <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="Innhold" 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">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> <button aria-controls="toc-Formell_definisjon-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 Formell definisjon</span> </button> <ul id="toc-Formell_definisjon-sublist" class="vector-toc-list"> <li id="toc-Notasjon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notasjon"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Notasjon</span> </div> </a> <ul id="toc-Notasjon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Veldefinerte_binære_operasjoner" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Veldefinerte_binære_operasjoner"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Veldefinerte binære operasjoner</span> </div> </a> <ul id="toc-Veldefinerte_binære_operasjoner-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Egenskaper_til_binære_operasjoner" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Egenskaper_til_binære_operasjoner"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Egenskaper til binære operasjoner</span> </div> </a> <button aria-controls="toc-Egenskaper_til_binære_operasjoner-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 Egenskaper til binære operasjoner</span> </button> <ul id="toc-Egenskaper_til_binære_operasjoner-sublist" class="vector-toc-list"> <li id="toc-Kommutativitet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kommutativitet"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Kommutativitet</span> </div> </a> <ul id="toc-Kommutativitet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Assosiativitet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Assosiativitet"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Assosiativitet</span> </div> </a> <ul id="toc-Assosiativitet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enhetselement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Enhetselement"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Enhetselement</span> </div> </a> <ul id="toc-Enhetselement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Invers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Invers"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Invers</span> </div> </a> <ul id="toc-Invers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Idempotens" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Idempotens"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Idempotens</span> </div> </a> <ul id="toc-Idempotens-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Regnearter_i_aritmetikk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Regnearter_i_aritmetikk"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Regnearter i aritmetikk</span> </div> </a> <ul id="toc-Regnearter_i_aritmetikk-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">4</span> <span>Referanser</span> </div> </a> <ul id="toc-Referanser-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">Binær operasjon</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 64 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-64" 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">64 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/Bin%C3%A6r_operasjon" title="Binær operasjon – norsk nynorsk" lang="nn" hreflang="nn" data-title="Binær operasjon" 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/Bin%C3%A6r_operator" title="Binær operator – dansk" lang="da" hreflang="da" data-title="Binær operator" 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/Bin%C3%A4r_operator" title="Binär operator – svensk" lang="sv" hreflang="sv" data-title="Binär operator" 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/A%C3%B0ger%C3%B0_(st%C3%A6r%C3%B0fr%C3%A6%C3%B0i)" title="Aðgerð (stærðfræði) – islandsk" lang="is" hreflang="is" data-title="Aðgerð (stærðfræði)" 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%AB%D9%86%D8%A7%D8%A6%D9%8A%D8%A9" title="عملية ثنائية – arabisk" lang="ar" hreflang="ar" data-title="عملية ثنائية" 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/Operaci%C3%B3n_binaria" title="Operación binaria – asturisk" lang="ast" hreflang="ast" data-title="Operación binaria" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%AA%E0%A6%BE%E0%A6%B0%E0%A7%87%E0%A6%B6%E0%A6%A8_(%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4)" title="অপারেশন (গণিত) – bengali" lang="bn" hreflang="bn" data-title="অপারেশন (গণিত)" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D1%96%D0%BD%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%8B%D1%8F" title="Бінарная аперацыя – belarusisk" lang="be" hreflang="be" data-title="Бінарная 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%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Бинарна операция – bulgarsk" lang="bg" hreflang="bg" data-title="Бинарна операция" 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/Binarna_operacija" title="Binarna operacija – bosnisk" lang="bs" hreflang="bs" data-title="Binarna operacija" 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/Operaci%C3%B3_bin%C3%A0ria" title="Operació binària – katalansk" lang="ca" hreflang="ca" data-title="Operació binària" 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%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BB%C4%83_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8" title="Бинарлă операци – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Бинарлă операци" 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/Bin%C3%A1rn%C3%AD_operace" title="Binární operace – tsjekkisk" lang="cs" hreflang="cs" data-title="Binární operace" 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/Zweistellige_Verkn%C3%BCpfung" title="Zweistellige Verknüpfung – tysk" lang="de" hreflang="de" data-title="Zweistellige Verknüpfung" 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/Binaarne_tehe" title="Binaarne tehe – estisk" lang="et" hreflang="et" data-title="Binaarne tehe" 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%94%CF%85%CE%B1%CE%B4%CE%B9%CE%BA%CE%AE_%CF%80%CF%81%CE%AC%CE%BE%CE%B7" title="Δυαδική πράξη – gresk" lang="el" hreflang="el" data-title="Δυαδική πράξη" 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/Binary_operation" title="Binary operation – engelsk" lang="en" hreflang="en" data-title="Binary operation" 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/Operaci%C3%B3n_binaria" title="Operación binaria – spansk" lang="es" hreflang="es" data-title="Operación binaria" 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/Duvalenta_operacio" title="Duvalenta operacio – esperanto" lang="eo" hreflang="eo" data-title="Duvalenta operacio" 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/Eragiketa_bitar" title="Eragiketa bitar – baskisk" lang="eu" hreflang="eu" data-title="Eragiketa bitar" 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%B9%D9%85%D9%84_%D8%AF%D9%88%D8%AA%D8%A7%DB%8C%DB%8C" title="عمل دوتایی – persisk" lang="fa" hreflang="fa" data-title="عمل دوتایی" 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/Op%C3%A9ration_binaire" title="Opération binaire – fransk" lang="fr" hreflang="fr" data-title="Opération binaire" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Obrachadh_c%C3%A0raideach" title="Obrachadh càraideach – skotsk-gælisk" lang="gd" hreflang="gd" data-title="Obrachadh càraideach" data-language-autonym="Gàidhlig" data-language-local-name="skotsk-gælisk" 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/Operaci%C3%B3n_binaria" title="Operación binaria – galisisk" lang="gl" hreflang="gl" data-title="Operación binaria" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Бинарн операция – kalmukkisk" lang="xal" hreflang="xal" data-title="Бинарн операция" data-language-autonym="Хальмг" data-language-local-name="kalmukkisk" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-ko badge-Q70893996 mw-list-item" title=""><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%ED%95%AD_%EC%97%B0%EC%82%B0" title="이항 연산 – koreansk" lang="ko" hreflang="ko" data-title="이항 연산" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Binarna_operacija" title="Binarna operacija – kroatisk" lang="hr" hreflang="hr" data-title="Binarna operacija" 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/Operasi_biner" title="Operasi biner – indonesisk" lang="id" hreflang="id" data-title="Operasi biner" 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/Operation_binari" title="Operation binari – interlingua" lang="ia" hreflang="ia" data-title="Operation binari" 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/Operazione_binaria" title="Operazione binaria – italiensk" lang="it" hreflang="it" data-title="Operazione binaria" 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%91%D7%99%D7%A0%D7%90%D7%A8%D7%99%D7%AA" title="פעולה בינארית – hebraisk" lang="he" hreflang="he" data-title="פעולה בינארית" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Kiryar_(matemat%C3%AEk)" title="Kiryar (matematîk) – kurdisk" lang="ku" hreflang="ku" data-title="Kiryar (matematîk)" data-language-autonym="Kurdî" data-language-local-name="kurdisk" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bin%C4%81ra_oper%C4%81cija" title="Bināra operācija – latvisk" lang="lv" hreflang="lv" data-title="Bināra operācija" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A6%E0%B5%8D%E0%B4%B5%E0%B4%AF%E0%B4%BE%E0%B4%99%E0%B5%8D%E0%B4%95%E0%B4%B8%E0%B4%82%E0%B4%95%E0%B5%8D%E0%B4%B0%E0%B4%BF%E0%B4%AF" title="ദ്വയാങ്കസംക്രിയ – malayalam" lang="ml" hreflang="ml" data-title="ദ്വയാങ്കസംക്രിയ" 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/Operasi_dedua" title="Operasi dedua – malayisk" lang="ms" hreflang="ms" data-title="Operasi dedua" 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-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Operasi_biner" title="Operasi biner – minangkabau" lang="min" hreflang="min" data-title="Operasi biner" data-language-autonym="Minangkabau" data-language-local-name="minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Binaire_operatie" title="Binaire operatie – nederlandsk" lang="nl" hreflang="nl" data-title="Binaire operatie" 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/%E4%BA%8C%E9%A0%85%E6%BC%94%E7%AE%97" title="二項演算 – japansk" lang="ja" hreflang="ja" data-title="二項演算" 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/L%C3%A8i_de_composicion_int%C3%A8rna" title="Lèi de composicion intèrna – oksitansk" lang="oc" hreflang="oc" data-title="Lèi de composicion intèrna" data-language-autonym="Occitan" data-language-local-name="oksitansk" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Operassion" title="Operassion – piemontesisk" lang="pms" hreflang="pms" data-title="Operassion" data-language-autonym="Piemontèis" data-language-local-name="piemontesisk" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Dzia%C5%82anie_dwuargumentowe" title="Działanie dwuargumentowe – polsk" lang="pl" hreflang="pl" data-title="Działanie dwuargumentowe" 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/Opera%C3%A7%C3%A3o_bin%C3%A1ria" title="Operação binária – portugisisk" lang="pt" hreflang="pt" data-title="Operação binária" 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/Opera%C8%9Bie_binar%C4%83" title="Operație binară – rumensk" lang="ro" hreflang="ro" data-title="Operație binară" 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%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Бинарная операция – russisk" lang="ru" hreflang="ru" data-title="Бинарная операция" 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/Veprimi_binar" title="Veprimi binar – albansk" lang="sq" hreflang="sq" data-title="Veprimi binar" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Opirazzioni_binaria" title="Opirazzioni binaria – siciliansk" lang="scn" hreflang="scn" data-title="Opirazzioni binaria" data-language-autonym="Sicilianu" data-language-local-name="siciliansk" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Binary_operation" title="Binary operation – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Binary operation" 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/Bin%C3%A1rna_oper%C3%A1cia" title="Binárna operácia – slovakisk" lang="sk" hreflang="sk" data-title="Binárna operácia" 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/Dvo%C4%8Dlena_operacija" title="Dvočlena operacija – slovensk" lang="sl" hreflang="sl" data-title="Dvočlena operacija" 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/%DA%A9%D8%B1%D8%AF%D8%A7%D8%B1_(%D8%A8%DB%8C%D8%B1%DA%A9%D8%A7%D8%B1%DB%8C)" title="کردار (بیرکاری) – sentralkurdisk" lang="ckb" hreflang="ckb" data-title="کردار (بیرکاری)" 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%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Бинарна операција – serbisk" lang="sr" hreflang="sr" data-title="Бинарна операција" 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/Binarna_operacija" title="Binarna operacija – serbokroatisk" lang="sh" hreflang="sh" data-title="Binarna operacija" 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/Bin%C3%A4%C3%A4rioperaatio" title="Binäärioperaatio – finsk" lang="fi" hreflang="fi" data-title="Binäärioperaatio" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Operasyong_tambalan" title="Operasyong tambalan – tagalog" lang="tl" hreflang="tl" data-title="Operasyong tambalan" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%88%E0%AE%B0%E0%AF%81%E0%AE%B1%E0%AF%81%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%9A%E0%AF%8D_%E0%AE%9A%E0%AF%86%E0%AE%AF%E0%AE%B2%E0%AE%BF" title="ஈருறுப்புச் செயலி – tamil" lang="ta" hreflang="ta" data-title="ஈருறுப்புச் செயலி" 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%81%E0%B8%B2%E0%B8%A3%E0%B8%94%E0%B8%B3%E0%B9%80%E0%B8%99%E0%B8%B4%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%97%E0%B8%A7%E0%B8%B4%E0%B8%A0%E0%B8%B2%E0%B8%84" title="การดำเนินการทวิภาค – thai" lang="th" hreflang="th" data-title="การดำเนินการทวิภาค" 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/%C4%B0kili_i%C5%9Flem" title="İkili işlem – tyrkisk" lang="tr" hreflang="tr" data-title="İkili işlem" 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%91%D1%96%D0%BD%D0%B0%D1%80%D0%BD%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%96%D1%8F" title="Бінарна операція – ukrainsk" lang="uk" hreflang="uk" data-title="Бінарна операція" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A9p_to%C3%A1n_hai_ng%C3%B4i" title="Phép toán hai ngôi – vietnamesisk" lang="vi" hreflang="vi" data-title="Phép toán hai ngôi" 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-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97" title="二元運算 – klassisk kinesisk" lang="lzh" hreflang="lzh" data-title="二元運算" data-language-autonym="文言" data-language-local-name="klassisk kinesisk" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97" title="二元运算 – wu" lang="wuu" hreflang="wuu" data-title="二元运算" 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%91%D7%99%D7%A0%D7%90%D7%A8%D7%99%D7%A9%D7%A2_%D7%90%D7%A4%D7%A2%D7%A8%D7%90%D7%A6%D7%99%D7%A2" title="בינארישע אפעראציע – jiddisk" lang="yi" hreflang="yi" data-title="בינארישע אפעראציע" 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/%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97" title="二元運算 – kantonesisk" lang="yue" hreflang="yue" data-title="二元運算" 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/%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97" title="二元运算 – kinesisk" lang="zh" hreflang="zh" data-title="二元运算" 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/Q164307#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/Bin%C3%A6r_operasjon" 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:Bin%C3%A6r_operasjon&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" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Bytt språkvariant" > <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">norsk bokmål</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="Visninger"> <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/Bin%C3%A6r_operasjon"><span>Les</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=history" title="Tidligere sideversjoner av denne siden [h]" accesskey="h"><span>Vis historikk</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <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="Verktøy" > <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">Verktøy</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">Verktøy</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skjul</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Flere alternativer" > <div class="vector-menu-heading"> Handlinger </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/Bin%C3%A6r_operasjon"><span>Les</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Bin%C3%A6r_operasjon&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=Bin%C3%A6r_operasjon&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/Bin%C3%A6r_operasjon" 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/Bin%C3%A6r_operasjon" rel="nofollow" title="Siste endringer i sider som blir lenket fra denne siden [k]" accesskey="k"><span>Relaterte endringer</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=no" title="Last opp filer [u]" accesskey="u"><span>Last opp fil</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Spesial:Spesialsider" title="Liste over alle spesialsider [q]" accesskey="q"><span>Spesialsider</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Bin%C3%A6r_operasjon&oldid=15669615" title="Permanent lenke til denne versjonen av siden"><span>Permanent lenke</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=info" title="Mer informasjon om denne siden"><span>Sideinformasjon</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesial:Siteringshjelp&page=Bin%C3%A6r_operasjon&id=15669615&wpFormIdentifier=titleform" title="Informasjon om hvordan denne siden kan siteres"><span>Siter denne siden</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesial:UrlShortener&url=https%3A%2F%2Fno.wikipedia.org%2Fwiki%2FBin%25C3%25A6r_operasjon"><span>Hent forkortet URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spesial:QrCode&url=https%3A%2F%2Fno.wikipedia.org%2Fwiki%2FBin%25C3%25A6r_operasjon"><span>Last ned QR-kode</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"> Skriv ut / eksporter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Spesial:DownloadAsPdf&page=Bin%C3%A6r_operasjon&action=show-download-screen"><span>Last ned som PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Bin%C3%A6r_operasjon&printable=yes" title="Utskriftsvennlig versjon av denne siden [p]" accesskey="p"><span>Utskriftsvennlig versjon</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"> På andre prosjekter </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:Binary_operations" 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/Q164307" title="Lenke til koblet dataregisterelement [g]" accesskey="g"><span>Wikidata-element</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="Sideverktøy"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <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">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skjul</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">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>binær operasjon</b> eller en <b>binæroperasjon</b> er i <a href="/wiki/Matematikk" title="Matematikk">matematikk</a> en <a href="/wiki/Operasjon_(matematikk)" title="Operasjon (matematikk)">operasjon</a> som har <i>to</i> argumenter fra samme <a href="/wiki/Mengde" title="Mengde">mengde</a> og der også resultatet tilhører samme mengde. De grunnleggende aritmetiske regneartene <a href="/wiki/Addisjon" title="Addisjon">addisjon</a>, <a href="/wiki/Subtraksjon" title="Subtraksjon">subtraksjon</a>, <a href="/wiki/Multiplikasjon" title="Multiplikasjon">multiplikasjon</a> og <a href="/wiki/Divisjon_(matematikk)" title="Divisjon (matematikk)">divisjon</a> for <a href="/wiki/Reelt_tall" title="Reelt tall">reelle tall</a> er alle binære. </p><p>Den vanligste definisjonen av en binæroperasjon krever at resultatet ligger i samme mengde som argumentene. En del forfattere vil likevel bruke begrepet mer generelt om operasjoner som involverer to argument, uten hensyn til resultatet.<sup id="cite_ref-DM1_1-0" class="reference"><a href="#cite_note-DM1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Ifølge den første definisjonen vil <a href="/wiki/Indreprodukt" title="Indreprodukt">indreproduktet</a> mellom to <a href="/wiki/Vektor_(matematikk)" title="Vektor (matematikk)">vektorer</a> <i>ikke</i> være en binær operasjon, mens den vil være det ifølge den mer generelle definisjonen. </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=Bin%C3%A6r_operasjon&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=Bin%C3%A6r_operasjon&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>Formelt kan en definere en binær operasjon som en <a href="/wiki/Funksjon_(matematikk)" title="Funksjon (matematikk)">funksjon</a> f: <i>M</i> × <i>M</i> → <i>M</i>. Denne funksjonen har <a href="/wiki/Aritet" title="Aritet">aritet</a> lik 2, det vil si at den tar <i>to</i> argument. </p><p>Mengden <i>M</i> kalles <a href="/wiki/Definisjonsmengde" title="Definisjonsmengde">definisjonsmengden</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Notasjon">Notasjon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=2" title="Rediger avsnitt: Notasjon" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=2" title="Rediger kildekoden til seksjonen Notasjon"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dersom (<i>a</i>,<i>b</i>) er et <a href="/wiki/Ordnede_par" title="Ordnede par">ordnet par</a> i det <a href="/wiki/Kartesisk_produkt" title="Kartesisk produkt">kartesiske produktet</a> <i>M</i> × <i>M</i> kan en skrive en generell 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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> på formen </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 a\ast b=\ast (a,b)\in M\quad \forall a,b\in M.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∗</mo> <mi>b</mi> <mo>=</mo> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>M</mi> <mspace width="1em" /> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>∈</mo> <mi>M</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\ast b=\ast (a,b)\in M\quad \forall a,b\in M.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a514e42220971966e756459c7995d50c90cc071" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.23ex; height:2.843ex;" alt="{\displaystyle a\ast b=\ast (a,b)\in M\quad \forall a,b\in M.\,}"></span></dd></dl> <p>Når operatorsymbolet <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> i en binær operasjon plasseres <i>mellom</i> argumentene kalles notasjonen for <i>infiks</i>, og dette er den vanligste skriveformen. En <i>prefiks</i>- og en <i>postfiks</i> notasjon er også mulig, med operatorsymbolet plassert henholdsvis før eller etter det ordnede paret. <a href="/wiki/Polsk_notasjon" title="Polsk notasjon">Polsk notasjon</a> bruker prefiks notasjon, mens <a href="/wiki/Omvendt_polsk_notasjon" title="Omvendt polsk notasjon">omvendt polsk notasjon</a> er basert på postfiks. </p> <div class="mw-heading mw-heading3"><h3 id="Veldefinerte_binære_operasjoner"><span id="Veldefinerte_bin.C3.A6re_operasjoner"></span>Veldefinerte binære operasjoner</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=3" title="Rediger avsnitt: Veldefinerte binære operasjoner" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=3" title="Rediger kildekoden til seksjonen Veldefinerte binære operasjoner"><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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> er <i>veldefinert</i> dersom <i>a</i> = <i>b</i> og <i>c</i> = <i>d</i> medfører at <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span>(a,c) = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span>(b,d). All vanlige binære operasjoner er veldefinerte. </p><p>Et eksempel på en binær operasjon som <i>ikke</i> er veldefinert er gitt ved det følgende definisjonen av en addisjonsoperasjon i mengden av <a href="/wiki/Rasjonalt_tall" title="Rasjonalt tall">rasjonale tall</a>: </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 {\frac {x}{y}}+{\frac {a}{b}}={\frac {x+a}{y+b}}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>y</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>+</mo> <mi>a</mi> </mrow> <mrow> <mi>y</mi> <mo>+</mo> <mi>b</mi> </mrow> </mfrac> </mrow> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x}{y}}+{\frac {a}{b}}={\frac {x+a}{y+b}}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96f1a5df00a20aba977dc159f0d01d370adb286b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.441ex; height:5.509ex;" alt="{\displaystyle {\frac {x}{y}}+{\frac {a}{b}}={\frac {x+a}{y+b}}.\,}"></span></dd></dl> <p>At definisjonen ikke er veldefinert ser en ved å bruke <i>x</i>/<i>y</i> = 1/3 = 2/6 og <i>a</i>/<i>b</i> = 1/2 = 7/14. </p> <div class="mw-heading mw-heading2"><h2 id="Egenskaper_til_binære_operasjoner"><span id="Egenskaper_til_bin.C3.A6re_operasjoner"></span>Egenskaper til binære operasjoner</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=4" title="Rediger avsnitt: Egenskaper til binære operasjoner" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=4" title="Rediger kildekoden til seksjonen Egenskaper til binære operasjoner"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Kommutativitet">Kommutativitet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=5" title="Rediger avsnitt: Kommutativitet" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=5" title="Rediger kildekoden til seksjonen Kommutativitet"><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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> er <a href="/wiki/Kommutativ_lov" title="Kommutativ lov">kommutativ</a> i <i>M</i> dersom den følgende relasjonen er oppfylt: </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 \ast (a,b)=\ast (b,a)\quad \forall a,b\in M.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>,</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>∈</mo> <mi>M</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast (a,b)=\ast (b,a)\quad \forall a,b\in M.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b346bd49ecab5b357857e2b945a2e9f679e5bd56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.758ex; height:2.843ex;" alt="{\displaystyle \ast (a,b)=\ast (b,a)\quad \forall a,b\in M.\,}"></span></dd></dl> <p>Addisjon av reelle tall er kommutativ, mens divisjon ikke er det. </p> <div class="mw-heading mw-heading3"><h3 id="Assosiativitet">Assosiativitet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=6" title="Rediger avsnitt: Assosiativitet" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=6" title="Rediger kildekoden til seksjonen Assosiativitet"><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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> er <a href="/wiki/Assosiativ_lov" title="Assosiativ lov">assosiativ</a> i <i>M</i> dersom </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ast (a,\ast (b,c))=\ast (\ast (a,b),c)\quad \forall a,b,c\in M.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∗</mo> <mo stretchy="false">(</mo> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>∈</mo> <mi>M</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast (a,\ast (b,c))=\ast (\ast (a,b),c)\quad \forall a,b,c\in M.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1761f9bc07ab23f30fdb2ccc0a6e66446d91e221" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.824ex; height:2.843ex;" alt="{\displaystyle \ast (a,\ast (b,c))=\ast (\ast (a,b),c)\quad \forall a,b,c\in M.\,}"></span> </p><p>Addisjon av reelle tall er assosiativ, mens subtraksjon ikke er assosiativ. </p> <div class="mw-heading mw-heading3"><h3 id="Enhetselement">Enhetselement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=7" title="Rediger avsnitt: Enhetselement" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=7" title="Rediger kildekoden til seksjonen Enhetselement"><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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> har et <i>enhetselement</i> dersom det eksisterer et element <i>e</i> i <i>M</i>, slik at </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 \ast (a,e)=\ast (e,a)=a\quad \forall a\in M.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>e</mi> <mo>,</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mspace width="1em" /> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>M</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast (a,e)=\ast (e,a)=a\quad \forall a\in M.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/423e289177bc9d37b4a029638fd268b905c12f31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.226ex; height:2.843ex;" alt="{\displaystyle \ast (a,e)=\ast (e,a)=a\quad \forall a\in M.\,}"></span></dd></dl> <p>Addisjon av reelle tall har enhetselementet 0. Subtraksjon har ikke noe enhetselement. Enhetselement kalles også for <i>nøytralelement</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Invers">Invers</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=8" title="Rediger avsnitt: Invers" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=8" title="Rediger kildekoden til seksjonen Invers"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dersom 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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> har enhetselement <i>e</i>, så kan et element <i>a</i> i <i>M</i> ha en <i>invers</i> betegnet med <i>a</i><sup>-1</sup>, 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 \ast (a,a^{-1})=\ast (a^{-1},a)=e.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∗</mo> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>e</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast (a,a^{-1})=\ast (a^{-1},a)=e.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aac745d1a6388c5ff0a37f8135a493f05b02a36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.523ex; height:3.176ex;" alt="{\displaystyle \ast (a,a^{-1})=\ast (a^{-1},a)=e.}"></span></dd></dl> <p>Det er mulig at enkelte element i <i>M</i> har en invers, mens andre ikke har det. </p> <div class="mw-heading mw-heading3"><h3 id="Idempotens">Idempotens</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=9" title="Rediger avsnitt: Idempotens" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=9" title="Rediger kildekoden til seksjonen Idempotens"><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 \ast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1858484bef51b1435c2b986c728a81788051803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \ast }"></span> er <i>idempotent</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 \ast (a,a)=a\quad \forall a\in M.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mspace width="1em" /> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>M</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ast (a,a)=a\quad \forall a\in M.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a149773cd87beaa45ddbf88feb15bbbe4faf6b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.955ex; height:2.843ex;" alt="{\displaystyle \ast (a,a)=a\quad \forall a\in M.\,}"></span></dd></dl> <p>Operasjonen som tar maksimumsverdien av to reelle tall er idempotent, da <i>max</i>(<i>a</i>,<i>a</i>) = <i>a</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Regnearter_i_aritmetikk">Regnearter i aritmetikk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&veaction=edit&section=10" title="Rediger avsnitt: Regnearter i aritmetikk" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=10" title="Rediger kildekoden til seksjonen Regnearter i aritmetikk"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I <a href="/wiki/Aritmetikk" title="Aritmetikk">aritmetikk</a> regner man med fire grunnleggende <i>regnearter</i>, som alle er binære operasjoner: </p> <dl><dt><a href="/wiki/Addisjon" title="Addisjon">Addisjon</a></dt></dl> <ul><li>Addend + addend = sum</li></ul> <p>Addisjon i mengden av <a href="/wiki/Reelt_tall" title="Reelt tall">reelle tall</a> <b>R</b> er kommutativ, assosiativ og har enhetselementet 0. </p> <dl><dt><a href="/wiki/Subtraksjon" title="Subtraksjon">Subtraksjon</a></dt></dl> <ul><li>Minuend − subtrahend = differanse</li></ul> <p>Subtraksjon i <b>R</b> er hverken kommutativ eller assosiativ, og operasjonen har ikke enhetselement. </p> <dl><dt><a href="/wiki/Multiplikasjon" title="Multiplikasjon">Multiplikasjon</a></dt></dl> <ul><li>Faktor × faktor = produkt</li></ul> <p>Multiplikasjon i <b>R</b> er kommutativ og assosiativ, med enhetselement 1. </p> <dl><dt><a href="/wiki/Divisjon_(matematikk)" title="Divisjon (matematikk)">Divisjon</a></dt></dl> <ul><li>Dividend / divisor = kvotient</li></ul> <p>Divisjon i <b>R</b> er hverken kommutativ eller assosiativ, og operasjonen har ikke enhetselement. </p> <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=Bin%C3%A6r_operasjon&veaction=edit&section=11" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6r_operasjon&action=edit&section=11" 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-DM1-1"><b><a href="#cite_ref-DM1_1-0">^</a></b> <span class="reference-text"><cite class="citation book">E.J.Borowski, J.M.Borwein (1989). <i>Dictionary of mathematics</i>. Glasgow: Collins. s. 53. <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%3ABin%C3%A6r+operasjon&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.pages=53&rft.place=Glasgow&rft.pub=Collins&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> [<i>Binary operations</i>]</span> </li> </ol></div> <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 .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r24561737">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}</style></div><div role="navigation" class="navbox" aria-labelledby="Oppslagsverk/autoritetsdata" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Oppslagsverk/autoritetsdata" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hjelp:Autoritetsdata" title="Hjelp:Autoritetsdata">Oppslagsverk/autoritetsdata</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0em 0.25em"><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/dyadic-operator">Encyclopædia Britannica</a> <b>·</b> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/BinaryOperation.html">MathWorld</a> <b>·</b> <a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph118879">NKC</a></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Hentet fra «<a dir="ltr" href="https://no.wikipedia.org/w/index.php?title=Binær_operasjon&oldid=15669615">https://no.wikipedia.org/w/index.php?title=Binær_operasjon&oldid=15669615</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Kategori:Kategorier" title="Kategori:Kategorier">Kategorier</a>: <ul><li><a href="/wiki/Kategori:Algebra" title="Kategori:Algebra">Algebra</a></li><li><a href="/wiki/Kategori:Bin%C3%A6re_operasjoner" title="Kategori:Binære operasjoner">Binære operasjoner</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skjult kategori: <ul><li><a href="/wiki/Kategori:Artikler_med_autoritetsdatalenker_fra_Wikidata" title="Kategori:Artikler med autoritetsdatalenker fra Wikidata">Artikler med autoritetsdatalenker fra Wikidata</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"> Denne siden ble sist redigert 15. jan. 2016 kl. 18:05.</li> <li id="footer-info-copyright">Innholdet er tilgjengelig under <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.no">Creative Commons-lisensen Navngivelse-DelPåSammeVilkår</a>, men ytterligere betingelser kan gjelde. Se <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">bruksvilkårene</a> for detaljer.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Personvern</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:Om">Om Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Generelle_forbehold">Forbehold</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Atferdsnorm</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Utviklere</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/no.wikipedia.org">Statistikk</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Erklæring om informasjonskapsler</a></li> <li id="footer-places-mobileview"><a href="//no.m.wikipedia.org/w/index.php?title=Bin%C3%A6r_operasjon&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobilvisning</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"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></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"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-6df7948d6c-kvpkk","wgBackendResponseTime":196,"wgPageParseReport":{"limitreport":{"cputime":"0.228","walltime":"0.355","ppvisitednodes":{"value":941,"limit":1000000},"postexpandincludesize":{"value":6341,"limit":2097152},"templateargumentsize":{"value":408,"limit":2097152},"expansiondepth":{"value":8,"limit":100},"expensivefunctioncount":{"value":3,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":6172,"limit":5000000},"entityaccesscount":{"value":4,"limit":400},"timingprofile":["100.00% 250.141 1 -total"," 72.52% 181.412 1 Mal:Autoritetsdata"," 39.10% 97.810 1 Mal:Navboks"," 37.27% 93.232 1 Mal:Navbox"," 26.09% 65.255 1 Mal:Kilde_bok"]},"scribunto":{"limitreport-timeusage":{"value":"0.153","limit":"10.000"},"limitreport-memusage":{"value":3786270,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-6b6c9bdc8b-9rndx","timestamp":"20241102183110","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Bin\u00e6r operasjon","url":"https:\/\/no.wikipedia.org\/wiki\/Bin%C3%A6r_operasjon","sameAs":"http:\/\/www.wikidata.org\/entity\/Q164307","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q164307","author":{"@type":"Organization","name":"Bidragsytere til Wikimedia-prosjektene"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-01-09T04:59:34Z","dateModified":"2016-01-15T17:05:21Z"}</script> </body> </html>