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="eu" dir="ltr"> <head> <meta charset="UTF-8"> <title>Zenbaki - Wikipedia, entziklopedia askea.</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(/(?:^|; )euwikimwclientpreferences=([^;]+)/);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":["","urtarrila","otsaila","martxoa","apirila","maiatza","ekaina","uztaila","abuztua","iraila","urria","azaroa","abendua"],"wgRequestId":"12c9b4f2-96b8-401c-a277-6fdf6bbaca70","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Zenbaki","wgTitle":"Zenbaki","wgCurRevisionId":9348011,"wgRevisionId":9348011,"wgArticleId":2918,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Wikipedia guztiek izan beharreko artikuluak","Hezkuntza Programako artikuluak","Hezkuntza Programa/Matematika","Wikipedia:BNE identifikatzailea duten artikuluak","Wikipedia:BNF identifikatzailea duten artikuluak","Wikipedia:GND identifikatzailea duten artikuluak","Wikipedia:LCCN identifikatzailea duten artikuluak","Wikipedia:AAT identifikatzailea duten artikuluak","Jakindunen bideoak dituzten artikuluak","Zenbakiak","Objektu matematikoak"],"wgPageViewLanguage":"eu", "wgPageContentLanguage":"eu","wgPageContentModel":"wikitext","wgRelevantPageName":"Zenbaki","wgRelevantArticleId":2918,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"eu","pageLanguageDir":"ltr","pageVariantFallbacks":"eu"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":30000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q11563","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform", "platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","ext.cite.styles":"ready","mediawiki.page.gallery.styles":"ready","ext.tmh.player.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","mediawiki.page.gallery","ext.tmh.player","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp", "ext.gadget.ErrefAurrebista","ext.gadget.UkensKonkurranse","ext.gadget.TxikipediaTab","ext.gadget.ArtikuluenKalitatea","ext.gadget.refToolbar","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=eu&modules=ext.cite.styles%7Cext.math.styles%7Cext.tmh.player.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cmediawiki.page.gallery.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=eu&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=eu&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.6"> <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 property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/-bertsomate-_Zenbaki_motak.webm/1200px---bertsomate-_Zenbaki_motak.webm.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="675"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/-bertsomate-_Zenbaki_motak.webm/800px---bertsomate-_Zenbaki_motak.webm.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="450"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/-bertsomate-_Zenbaki_motak.webm/640px---bertsomate-_Zenbaki_motak.webm.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="360"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Zenbaki - Wikipedia, entziklopedia askea."> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//eu.m.wikipedia.org/wiki/Zenbaki"> <link rel="alternate" type="application/x-wiki" title="Aldatu" href="/w/index.php?title=Zenbaki&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 (eu)"> <link rel="EditURI" type="application/rsd+xml" href="//eu.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://eu.wikipedia.org/wiki/Zenbaki"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.eu"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom Jarioa" href="/w/index.php?title=Berezi:AzkenAldaketak&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-Zenbaki rootpage-Zenbaki skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Edukira joan</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="Gunea"> <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="Menu nagusia" > <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">Menu nagusia</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">Menu nagusia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">ezkutatu</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Nabigazioa </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Azala" title="Azala bisitatu [z]" accesskey="z"><span>Azala</span></a></li><li id="n-Txikipedia" class="mw-list-item"><a href="/wiki/Txikipedia:Azala"><span>Txikipedia</span></a></li><li id="n-Ikusgela" class="mw-list-item"><a href="/wiki/Atari:Hezkuntza/Ikusgela"><span>Ikusgela</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Txokoa" title="Proiektuaren inguruan, zer egin dezakezu, non aurkitu nahi duzuna"><span>Txokoa</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Berezi:AzkenAldaketak" title="Wikiko azken aldaketen zerrenda. [r]" accesskey="r"><span>Aldaketa berriak</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Berezi:Ausazkoa" title="Ausazko orrialde bat kargatu [x]" accesskey="x"><span>Ausazko orria</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Laguntza:Sarrera" title="Aurkitzeko lekua."><span>Laguntza</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Azala" 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="Entziklopedia askea" src="/static/images/mobile/copyright/wikipedia-tagline-eu.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Berezi:Bilatu" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Wikipedia(e)n bilatu [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Bilatu</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="Wikipedia wikian bilatu" aria-label="Wikipedia wikian bilatu" autocapitalize="sentences" title="Wikipedia(e)n bilatu [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Berezi:Bilatu"> </div> <button class="cdx-button cdx-search-input__end-button">Bilatu</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Tresna pertsonalak"> <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="Itxura"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Itxura" > <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">Itxura</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=eu.wikipedia.org&uselang=eu" class=""><span>Dohaintza egin</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=Berezi:KontuaSortu&returnto=Zenbaki" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; ez da ezinbestekoa, ordea." class=""><span>Sortu kontua</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=Berezi:SaioaHasi&returnto=Zenbaki" title="Izen ematera gonbidatzen zaitugu. [o]" accesskey="o" class=""><span>Hasi saioa</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Aukera gehiago" > <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="Tresna pertsonalak" > <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">Tresna pertsonalak</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=eu.wikipedia.org&uselang=eu"><span>Dohaintza egin</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Berezi:KontuaSortu&returnto=Zenbaki" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; ez da ezinbestekoa, ordea."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Sortu kontua</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Berezi:SaioaHasi&returnto=Zenbaki" title="Izen ematera gonbidatzen zaitugu. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Hasi saioa</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Izena eman gabeko erabiltzaileentzako orrialdeak <a href="/wiki/Laguntza:Sarrera" aria-label="Artikuluak aldatzeari buruz gehiago ikasi"><span>gehiago ikasi</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Berezi:NireEkarpenak" title="IP helbide honetatik egindako aldaketen zerrenda [y]" accesskey="y"><span>Ekarpenak</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Berezi:NireEztabaida" title="Zure IParen eztabaida [n]" accesskey="n"><span>Eztabaida</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="Gunea"> <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="Edukiak" 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">Edukiak</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ezkutatu</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">⇑ Gora</div> </a> </li> <li id="toc-Zenbaki_kontzeptuaren_historia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zenbaki_kontzeptuaren_historia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Zenbaki kontzeptuaren historia</span> </div> </a> <button aria-controls="toc-Zenbaki_kontzeptuaren_historia-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>Erakutsi/ezkutatu Zenbaki kontzeptuaren historia azpiatal</span> </button> <ul id="toc-Zenbaki_kontzeptuaren_historia-sublist" class="vector-toc-list"> <li id="toc-Kontatzeko_lehen_siboloak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kontatzeko_lehen_siboloak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Kontatzeko lehen siboloak</span> </div> </a> <ul id="toc-Kontatzeko_lehen_siboloak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zeroaren_sorkuntza" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zeroaren_sorkuntza"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Zeroaren sorkuntza</span> </div> </a> <ul id="toc-Zeroaren_sorkuntza-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbaki_negatiboak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbaki_negatiboak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Zenbaki negatiboak</span> </div> </a> <ul id="toc-Zenbaki_negatiboak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zatikiak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zatikiak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Zatikiak</span> </div> </a> <ul id="toc-Zatikiak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbaki_konplexuak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbaki_konplexuak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Zenbaki konplexuak</span> </div> </a> <ul id="toc-Zenbaki_konplexuak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Indukzio_matematikoaren_printzipioa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Indukzio_matematikoaren_printzipioa"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Indukzio matematikoaren printzipioa</span> </div> </a> <ul id="toc-Indukzio_matematikoaren_printzipioa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Multzoen-teoria" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Multzoen-teoria"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.7</span> <span>Multzoen-teoria</span> </div> </a> <ul id="toc-Multzoen-teoria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Irrazionalen_teoriak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Irrazionalen_teoriak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.8</span> <span>Irrazionalen teoriak</span> </div> </a> <ul id="toc-Irrazionalen_teoriak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aljebra_hiperkonplexuak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aljebra_hiperkonplexuak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.9</span> <span>Aljebra hiperkonplexuak</span> </div> </a> <ul id="toc-Aljebra_hiperkonplexuak-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Zenbakien_sailkapena" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zenbakien_sailkapena"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Zenbakien sailkapena</span> </div> </a> <button aria-controls="toc-Zenbakien_sailkapena-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>Erakutsi/ezkutatu Zenbakien sailkapena azpiatal</span> </button> <ul id="toc-Zenbakien_sailkapena-sublist" class="vector-toc-list"> <li id="toc-Zenbaki_arruntak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbaki_arruntak"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Zenbaki arruntak</span> </div> </a> <ul id="toc-Zenbaki_arruntak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbaki_osoak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbaki_osoak"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Zenbaki osoak</span> </div> </a> <ul id="toc-Zenbaki_osoak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbaki_arrazionalak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbaki_arrazionalak"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Zenbaki arrazionalak</span> </div> </a> <ul id="toc-Zenbaki_arrazionalak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbaki_arrunt_bereziak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbaki_arrunt_bereziak"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Zenbaki arrunt bereziak</span> </div> </a> <ul id="toc-Zenbaki_arrunt_bereziak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Beste_zenbaki_batzuk" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Beste_zenbaki_batzuk"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Beste zenbaki batzuk</span> </div> </a> <ul id="toc-Beste_zenbaki_batzuk-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Beste_zenbaki_batzuk_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Beste_zenbaki_batzuk_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Beste zenbaki batzuk</span> </div> </a> <ul id="toc-Beste_zenbaki_batzuk_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Zenbakien_adierazpen_sistema" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zenbakien_adierazpen_sistema"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Zenbakien adierazpen sistema</span> </div> </a> <button aria-controls="toc-Zenbakien_adierazpen_sistema-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>Erakutsi/ezkutatu Zenbakien adierazpen sistema azpiatal</span> </button> <ul id="toc-Zenbakien_adierazpen_sistema-sublist" class="vector-toc-list"> <li id="toc-Zifra,_digitu_eta_zenbakizko" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zifra,_digitu_eta_zenbakizko"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Zifra, digitu eta zenbakizko</span> </div> </a> <ul id="toc-Zifra,_digitu_eta_zenbakizko-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbakizko_oinarria" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbakizko_oinarria"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Zenbakizko oinarria</span> </div> </a> <ul id="toc-Zenbakizko_oinarria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbakiak_hizkuntza_naturaletan" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbakiak_hizkuntza_naturaletan"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Zenbakiak hizkuntza naturaletan</span> </div> </a> <ul id="toc-Zenbakiak_hizkuntza_naturaletan-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ariketak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ariketak"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span><figcaption></figcaption><p> Ariketak</p></span> </div> </a> <ul id="toc-Ariketak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Erreferentziak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Erreferentziak"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Erreferentziak</span> </div> </a> <ul id="toc-Erreferentziak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ikus,_gainera" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ikus,_gainera"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Ikus, gainera</span> </div> </a> <ul id="toc-Ikus,_gainera-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kanpo_estekak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kanpo_estekak"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Kanpo estekak</span> </div> </a> <ul id="toc-Kanpo_estekak-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="Edukiak" 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="Eduki taularen ikusgarritasuna aldatu" > <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">Eduki taularen ikusgarritasuna aldatu</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">Zenbaki</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="Joan beste hizkuntza batean idatzitako artikulu batera. 189 hizkuntzatan eskuragarri." > <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-189" 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">189 hizkuntza</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Getal" title="Getal – afrikaansa" lang="af" hreflang="af" data-title="Getal" data-language-autonym="Afrikaans" data-language-local-name="afrikaansa" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Zahl" title="Zahl – Suitzako alemana" lang="gsw" hreflang="gsw" data-title="Zahl" data-language-autonym="Alemannisch" data-language-local-name="Suitzako alemana" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%89%81%E1%8C%A5%E1%88%AD" title="ቁጥር – amharera" lang="am" hreflang="am" data-title="ቁጥር" data-language-autonym="አማርኛ" data-language-local-name="amharera" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Numero" title="Numero – aragoiera" lang="an" hreflang="an" data-title="Numero" data-language-autonym="Aragonés" data-language-local-name="aragoiera" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/R%C4%ABm" title="Rīm – Old English" lang="ang" hreflang="ang" data-title="Rīm" data-language-autonym="Ænglisc" data-language-local-name="Old English" class="interlanguage-link-target"><span>Ænglisc</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="संख्या – angikera" lang="anp" hreflang="anp" data-title="संख्या" data-language-autonym="अंगिका" data-language-local-name="angikera" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF" title="عدد – arabiera" lang="ar" hreflang="ar" data-title="عدد" data-language-autonym="العربية" data-language-local-name="arabiera" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arc mw-list-item"><a href="https://arc.wikipedia.org/wiki/%DC%A1%DC%A2%DC%9D%DC%A2%DC%90" title="ܡܢܝܢܐ – Aramaic" lang="arc" hreflang="arc" data-title="ܡܢܝܢܐ" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="Aramaic" class="interlanguage-link-target"><span>ܐܪܡܝܐ</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="সংখ্যা – assamera" lang="as" hreflang="as" data-title="সংখ্যা" data-language-autonym="অসমীয়া" data-language-local-name="assamera" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/N%C3%BAmberu" title="Númberu – asturiera" lang="ast" hreflang="ast" data-title="Númberu" data-language-autonym="Asturianu" data-language-local-name="asturiera" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-atj mw-list-item"><a href="https://atj.wikipedia.org/wiki/Akitasowin" title="Akitasowin – atikamekwera" lang="atj" hreflang="atj" data-title="Akitasowin" data-language-autonym="Atikamekw" data-language-local-name="atikamekwera" class="interlanguage-link-target"><span>Atikamekw</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C6%8Fd%C9%99d" title="Ədəd – azerbaijanera" lang="az" hreflang="az" data-title="Ədəd" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijanera" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF" title="عدد – South Azerbaijani" lang="azb" hreflang="azb" data-title="عدد" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D2%BA%D0%B0%D0%BD" title="Һан – baxkirera" lang="ba" hreflang="ba" data-title="Һан" data-language-autonym="Башҡортса" data-language-local-name="baxkirera" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Zoih" title="Zoih – Bavarian" lang="bar" hreflang="bar" data-title="Zoih" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Skaitlios" title="Skaitlios – Samogitian" lang="sgs" hreflang="sgs" data-title="Skaitlios" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Bilang" title="Bilang – Central Bikol" lang="bcl" hreflang="bcl" data-title="Bilang" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9B%D1%96%D0%BA" title="Лік – bielorrusiera" lang="be" hreflang="be" data-title="Лік" data-language-autonym="Беларуская" data-language-local-name="bielorrusiera" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9B%D1%96%D0%BA" title="Лік – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Лік" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE" title="Число – bulgariera" lang="bg" hreflang="bg" data-title="Число" data-language-autonym="Български" data-language-local-name="bulgariera" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%A8%E0%A4%82%E0%A4%AC%E0%A4%B0" title="नंबर – Bhojpuri" lang="bh" hreflang="bh" data-title="नंबर" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/Wilangan" title="Wilangan – Banjar" lang="bjn" hreflang="bjn" data-title="Wilangan" data-language-autonym="Banjar" data-language-local-name="Banjar" class="interlanguage-link-target"><span>Banjar</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="সংখ্যা – bengalera" lang="bn" hreflang="bn" data-title="সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="bengalera" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%82%E0%BE%B2%E0%BD%84%E0%BD%A6%E0%BC%8B%E0%BD%80%E0%BC%8D" title="གྲངས་ཀ། – tibetera" lang="bo" hreflang="bo" data-title="གྲངས་ཀ།" data-language-autonym="བོད་ཡིག" data-language-local-name="tibetera" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Niver" title="Niver – bretoiera" lang="br" hreflang="br" data-title="Niver" data-language-autonym="Brezhoneg" data-language-local-name="bretoiera" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Broj" title="Broj – bosniera" lang="bs" hreflang="bs" data-title="Broj" data-language-autonym="Bosanski" data-language-local-name="bosniera" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BE" title="Тоо – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Тоо" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca badge-Q17437798 badge-goodarticle mw-list-item" title="artikulu onak"><a href="https://ca.wikipedia.org/wiki/Nombre" title="Nombre – katalana" lang="ca" hreflang="ca" data-title="Nombre" data-language-autonym="Català" data-language-local-name="katalana" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cbk-zam mw-list-item"><a href="https://cbk-zam.wikipedia.org/wiki/Numero" title="Numero – Chavacano" lang="cbk" hreflang="cbk" data-title="Numero" data-language-autonym="Chavacano de Zamboanga" data-language-local-name="Chavacano" class="interlanguage-link-target"><span>Chavacano de Zamboanga</span></a></li><li class="interlanguage-link interwiki-cho mw-list-item"><a href="https://cho.wikipedia.org/wiki/Hohltina" title="Hohltina – txoktawera" lang="cho" hreflang="cho" data-title="Hohltina" data-language-autonym="Chahta anumpa" data-language-local-name="txoktawera" class="interlanguage-link-target"><span>Chahta anumpa</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95" title="ژمارە – erdialdeko kurduera" lang="ckb" hreflang="ckb" data-title="ژمارە" data-language-autonym="کوردی" data-language-local-name="erdialdeko kurduera" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Numeru" title="Numeru – korsikera" lang="co" hreflang="co" data-title="Numeru" data-language-autonym="Corsu" data-language-local-name="korsikera" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cr mw-list-item"><a href="https://cr.wikipedia.org/wiki/%E1%90%8A%E1%91%AD%E1%90%A6%E1%91%96%E1%93%B1%E1%90%A3" title="ᐊᑭᐦᑖᓱᐣ – Cree" lang="cr" hreflang="cr" data-title="ᐊᑭᐦᑖᓱᐣ" data-language-autonym="Nēhiyawēwin / ᓀᐦᐃᔭᐍᐏᐣ" data-language-local-name="Cree" class="interlanguage-link-target"><span>Nēhiyawēwin / ᓀᐦᐃᔭᐍᐏᐣ</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C4%8C%C3%ADslo" title="Číslo – txekiera" lang="cs" hreflang="cs" data-title="Číslo" data-language-autonym="Čeština" data-language-local-name="txekiera" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cu mw-list-item"><a href="https://cu.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BC%D1%A7" title="Чисмѧ – elizako eslaviera" lang="cu" hreflang="cu" data-title="Чисмѧ" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="elizako eslaviera" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A5%D0%B8%D1%81%D0%B5%D0%BF" title="Хисеп – txuvaxera" lang="cv" hreflang="cv" data-title="Хисеп" data-language-autonym="Чӑвашла" data-language-local-name="txuvaxera" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhif" title="Rhif – galesa" lang="cy" hreflang="cy" data-title="Rhif" data-language-autonym="Cymraeg" data-language-local-name="galesa" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Tal" title="Tal – daniera" lang="da" hreflang="da" data-title="Tal" data-language-autonym="Dansk" data-language-local-name="daniera" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-dag mw-list-item"><a href="https://dag.wikipedia.org/wiki/Kalinli" title="Kalinli – Dagbani" lang="dag" hreflang="dag" data-title="Kalinli" data-language-autonym="Dagbanli" data-language-local-name="Dagbani" class="interlanguage-link-target"><span>Dagbanli</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Zahl" title="Zahl – alemana" lang="de" hreflang="de" data-title="Zahl" data-language-autonym="Deutsch" data-language-local-name="alemana" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-dty mw-list-item"><a href="https://dty.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95%E0%A4%BE" title="अंका – Doteli" lang="dty" hreflang="dty" data-title="अंका" data-language-autonym="डोटेली" data-language-local-name="Doteli" class="interlanguage-link-target"><span>डोटेली</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82" title="Αριθμός – greziera" lang="el" hreflang="el" data-title="Αριθμός" data-language-autonym="Ελληνικά" data-language-local-name="greziera" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/N%C3%B3mmer" title="Nómmer – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Nómmer" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Number" title="Number – ingelesa" lang="en" hreflang="en" data-title="Number" data-language-autonym="English" data-language-local-name="ingelesa" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Nombro" title="Nombro – esperantoa" lang="eo" hreflang="eo" data-title="Nombro" data-language-autonym="Esperanto" data-language-local-name="esperantoa" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero" title="Número – gaztelania" lang="es" hreflang="es" data-title="Número" data-language-autonym="Español" data-language-local-name="gaztelania" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Arv" title="Arv – estoniera" lang="et" hreflang="et" data-title="Arv" data-language-autonym="Eesti" data-language-local-name="estoniera" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/N%C3%BAmiru" title="Númiru – Extremaduran" lang="ext" hreflang="ext" data-title="Númiru" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF" title="عدد – persiera" lang="fa" hreflang="fa" data-title="عدد" data-language-autonym="فارسی" data-language-local-name="persiera" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ff mw-list-item"><a href="https://ff.wikipedia.org/wiki/Limle" title="Limle – fula" lang="ff" hreflang="ff" data-title="Limle" data-language-autonym="Fulfulde" data-language-local-name="fula" class="interlanguage-link-target"><span>Fulfulde</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Luku" title="Luku – finlandiera" lang="fi" hreflang="fi" data-title="Luku" data-language-autonym="Suomi" data-language-local-name="finlandiera" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Arv" title="Arv – Võro" lang="vro" hreflang="vro" data-title="Arv" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Naba" title="Naba – fijiera" lang="fj" hreflang="fj" data-title="Naba" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fijiera" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Tal" title="Tal – faroera" lang="fo" hreflang="fo" data-title="Tal" data-language-autonym="Føroyskt" data-language-local-name="faroera" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Nombre" title="Nombre – frantsesa" lang="fr" hreflang="fr" data-title="Nombre" data-language-autonym="Français" data-language-local-name="frantsesa" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frp mw-list-item"><a href="https://frp.wikipedia.org/wiki/Nombro" title="Nombro – Arpitan" lang="frp" hreflang="frp" data-title="Nombro" data-language-autonym="Arpetan" data-language-local-name="Arpitan" class="interlanguage-link-target"><span>Arpetan</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Taal" title="Taal – iparraldeko frisiera" lang="frr" hreflang="frr" data-title="Taal" data-language-autonym="Nordfriisk" data-language-local-name="iparraldeko frisiera" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Getal" title="Getal – mendebaldeko frisiera" lang="fy" hreflang="fy" data-title="Getal" data-language-autonym="Frysk" data-language-local-name="mendebaldeko frisiera" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Uimhir" title="Uimhir – irlandera" lang="ga" hreflang="ga" data-title="Uimhir" data-language-autonym="Gaeilge" data-language-local-name="irlandera" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%95%B8" title="數 – Gan" lang="gan" hreflang="gan" data-title="數" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Nomm" title="Nomm – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Nomm" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/%C3%80ireamh" title="Àireamh – Eskoziako gaelikoa" lang="gd" hreflang="gd" data-title="Àireamh" data-language-autonym="Gàidhlig" data-language-local-name="Eskoziako gaelikoa" 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/N%C3%BAmero" title="Número – galiziera" lang="gl" hreflang="gl" data-title="Número" data-language-autonym="Galego" data-language-local-name="galiziera" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Papapy" title="Papapy – guaraniera" lang="gn" hreflang="gn" data-title="Papapy" data-language-autonym="Avañe'ẽ" data-language-local-name="guaraniera" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-guc mw-list-item"><a href="https://guc.wikipedia.org/wiki/Nuumerokana" title="Nuumerokana – Wayuu" lang="guc" hreflang="guc" data-title="Nuumerokana" data-language-autonym="Wayuunaiki" data-language-local-name="Wayuu" class="interlanguage-link-target"><span>Wayuunaiki</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Lamba" title="Lamba – hausa" lang="ha" hreflang="ha" data-title="Lamba" data-language-autonym="Hausa" data-language-local-name="hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/N%C4%81_helu" title="Nā helu – hawaiiera" lang="haw" hreflang="haw" data-title="Nā helu" data-language-autonym="Hawaiʻi" data-language-local-name="hawaiiera" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8" title="מספר – hebreera" lang="he" hreflang="he" data-title="מספר" data-language-autonym="עברית" data-language-local-name="hebreera" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="संख्या – hindia" lang="hi" hreflang="hi" data-title="संख्या" data-language-autonym="हिन्दी" data-language-local-name="hindia" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Ginti" title="Ginti – Fiji Hindi" lang="hif" hreflang="hif" data-title="Ginti" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Broj" title="Broj – kroaziera" lang="hr" hreflang="hr" data-title="Broj" data-language-autonym="Hrvatski" data-language-local-name="kroaziera" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Nonm" title="Nonm – Haitiko kreolera" lang="ht" hreflang="ht" data-title="Nonm" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitiko kreolera" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sz%C3%A1m" title="Szám – hungariera" lang="hu" hreflang="hu" data-title="Szám" data-language-autonym="Magyar" data-language-local-name="hungariera" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B9%D5%AB%D5%BE" title="Թիվ – armeniera" lang="hy" hreflang="hy" data-title="Թիվ" data-language-autonym="Հայերեն" data-language-local-name="armeniera" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B9%D5%AB%D6%82" title="Թիւ – Western Armenian" lang="hyw" hreflang="hyw" data-title="Թիւ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Numero" title="Numero – interlingua" lang="ia" hreflang="ia" data-title="Numero" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Lumur" title="Lumur – ibanera" lang="iba" hreflang="iba" data-title="Lumur" data-language-autonym="Jaku Iban" data-language-local-name="ibanera" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan" title="Bilangan – indonesiera" lang="id" hreflang="id" data-title="Bilangan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiera" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Numero" title="Numero – ilocanoera" lang="ilo" hreflang="ilo" data-title="Numero" data-language-autonym="Ilokano" data-language-local-name="ilocanoera" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Nombro" title="Nombro – idoa" lang="io" hreflang="io" data-title="Nombro" data-language-autonym="Ido" data-language-local-name="idoa" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Tala_(st%C3%A6r%C3%B0fr%C3%A6%C3%B0i)" title="Tala (stærðfræði) – islandiera" lang="is" hreflang="is" data-title="Tala (stærðfræði)" data-language-autonym="Íslenska" data-language-local-name="islandiera" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero" title="Numero – italiera" lang="it" hreflang="it" data-title="Numero" data-language-autonym="Italiano" data-language-local-name="italiera" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%95%B0" title="数 – japoniera" lang="ja" hreflang="ja" data-title="数" data-language-autonym="日本語" data-language-local-name="japoniera" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Nomba" title="Nomba – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Nomba" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/namcu" title="namcu – lojbana" lang="jbo" hreflang="jbo" data-title="namcu" data-language-autonym="La .lojban." data-language-local-name="lojbana" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Wilangan_(mat%C3%A9matika)" title="Wilangan (matématika) – javera" lang="jv" hreflang="jv" data-title="Wilangan (matématika)" data-language-autonym="Jawa" data-language-local-name="javera" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%98" title="რიცხვი – georgiera" lang="ka" hreflang="ka" data-title="რიცხვი" data-language-autonym="ქართული" data-language-local-name="georgiera" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/San" title="San – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="San" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Am%E1%B8%8Dan" title="Amḍan – kabiliera" lang="kab" hreflang="kab" data-title="Amḍan" data-language-autonym="Taqbaylit" data-language-local-name="kabiliera" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/%C3%91%CA%8A%CA%8A_(t%CA%8A%CA%8Az%CA%8A%CA%8A)" title="Ñʊʊ (tʊʊzʊʊ) – Kabiye" lang="kbp" hreflang="kbp" data-title="Ñʊʊ (tʊʊzʊʊ)" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BD" title="Сан – kazakhera" lang="kk" hreflang="kk" data-title="Сан" data-language-autonym="Қазақша" data-language-local-name="kazakhera" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B3%86" title="ಸಂಖ್ಯೆ – kannada" lang="kn" hreflang="kn" data-title="ಸಂಖ್ಯೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%98_(%EC%88%98%ED%95%99)" title="수 (수학) – koreera" lang="ko" hreflang="ko" data-title="수 (수학)" data-language-autonym="한국어" data-language-local-name="koreera" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Hejmar" title="Hejmar – kurduera" lang="ku" hreflang="ku" data-title="Hejmar" data-language-autonym="Kurdî" data-language-local-name="kurduera" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Niver" title="Niver – kornubiera" lang="kw" hreflang="kw" data-title="Niver" data-language-autonym="Kernowek" data-language-local-name="kornubiera" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numerus" title="Numerus – latina" lang="la" hreflang="la" data-title="Numerus" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Zuel" title="Zuel – luxenburgera" lang="lb" hreflang="lb" data-title="Zuel" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxenburgera" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lbe mw-list-item"><a href="https://lbe.wikipedia.org/wiki/%D0%90%D1%8C%D0%B4%D0%B0%D0%B4" title="Аьдад – Lak" lang="lbe" hreflang="lbe" data-title="Аьдад" data-language-autonym="Лакку" data-language-local-name="Lak" class="interlanguage-link-target"><span>Лакку</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Numero" title="Numero – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Numero" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Ennamba" title="Ennamba – luganda" lang="lg" hreflang="lg" data-title="Ennamba" data-language-autonym="Luganda" data-language-local-name="luganda" class="interlanguage-link-target"><span>Luganda</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Getal" title="Getal – limburgera" lang="li" hreflang="li" data-title="Getal" data-language-autonym="Limburgs" data-language-local-name="limburgera" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Numer" title="Numer – Lombard" lang="lmo" hreflang="lmo" data-title="Numer" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%88%E0%BA%B3%E0%BA%99%E0%BA%A7%E0%BA%99" title="ຈຳນວນ – laosera" lang="lo" hreflang="lo" data-title="ຈຳນວນ" data-language-autonym="ລາວ" data-language-local-name="laosera" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Skai%C4%8Dius" title="Skaičius – lituaniera" lang="lt" hreflang="lt" data-title="Skaičius" data-language-autonym="Lietuvių" data-language-local-name="lituaniera" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Skaitlis" title="Skaitlis – letoniera" lang="lv" hreflang="lv" data-title="Skaitlis" data-language-autonym="Latviešu" data-language-local-name="letoniera" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95" title="अंक – maithilia" lang="mai" hreflang="mai" data-title="अंक" data-language-autonym="मैथिली" data-language-local-name="maithilia" class="interlanguage-link-target"><span>मैथिली</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Isa" title="Isa – malgaxea" lang="mg" hreflang="mg" data-title="Isa" data-language-autonym="Malagasy" data-language-local-name="malgaxea" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%A8%D0%BE%D1%82%D0%BF%D0%B0%D0%BB" title="Шотпал – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Шотпал" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D1%80%D0%BE%D1%98" title="Број – mazedoniera" lang="mk" hreflang="mk" data-title="Број" data-language-autonym="Македонски" data-language-local-name="mazedoniera" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF" title="സംഖ്യ – malabarera" lang="ml" hreflang="ml" data-title="സംഖ്യ" data-language-autonym="മലയാളം" data-language-local-name="malabarera" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BE" title="Тоо – mongoliera" lang="mn" hreflang="mn" data-title="Тоо" data-language-autonym="Монгол" data-language-local-name="mongoliera" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="संख्या – marathera" lang="mr" hreflang="mr" data-title="संख्या" data-language-autonym="मराठी" data-language-local-name="marathera" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Nombor" title="Nombor – malaysiera" lang="ms" hreflang="ms" data-title="Nombor" data-language-autonym="Bahasa Melayu" data-language-local-name="malaysiera" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/N%C3%BAmaro" title="Númaro – mirandesa" lang="mwl" hreflang="mwl" data-title="Númaro" data-language-autonym="Mirandés" data-language-local-name="mirandesa" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%80%E1%80%AD%E1%80%94%E1%80%BA%E1%80%B8" title="ကိန်း – birmaniera" lang="my" hreflang="my" data-title="ကိန်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmaniera" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D8%A7%D8%B4%D9%85%D8%A7%D8%B1%DA%A9" title="اشمارک – mazandarandera" lang="mzn" hreflang="mzn" data-title="اشمارک" data-language-autonym="مازِرونی" data-language-local-name="mazandarandera" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-nah mw-list-item"><a href="https://nah.wikipedia.org/wiki/Tlapohualli" title="Tlapohualli – Nahuatl" lang="nah" hreflang="nah" data-title="Tlapohualli" data-language-autonym="Nāhuatl" data-language-local-name="Nahuatl" class="interlanguage-link-target"><span>Nāhuatl</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Tahl" title="Tahl – behe-alemana" lang="nds" hreflang="nds" data-title="Tahl" data-language-autonym="Plattdüütsch" data-language-local-name="behe-alemana" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%85%E0%A4%99%E0%A5%8D%E0%A4%95" title="अङ्क – nepalera" lang="ne" hreflang="ne" data-title="अङ्क" data-language-autonym="नेपाली" data-language-local-name="nepalera" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B2%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%83" title="ल्याः – newarera" lang="new" hreflang="new" data-title="ल्याः" data-language-autonym="नेपाल भाषा" data-language-local-name="newarera" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Getal_(wiskunde)" title="Getal (wiskunde) – nederlandera" lang="nl" hreflang="nl" data-title="Getal (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="nederlandera" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Tal" title="Tal – nynorsk (norvegiera)" lang="nn" hreflang="nn" data-title="Tal" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk (norvegiera)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Tall" title="Tall – bokmål (norvegiera)" lang="nb" hreflang="nb" data-title="Tall" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål (norvegiera)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Nombre" title="Nombre – Novial" lang="nov" hreflang="nov" data-title="Nombre" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-nrm mw-list-item"><a href="https://nrm.wikipedia.org/wiki/Neunm%C3%A9tho" title="Neunmétho – Norman" lang="nrf" hreflang="nrf" data-title="Neunmétho" data-language-autonym="Nouormand" data-language-local-name="Norman" class="interlanguage-link-target"><span>Nouormand</span></a></li><li class="interlanguage-link interwiki-nso mw-list-item"><a href="https://nso.wikipedia.org/wiki/Nomoro" title="Nomoro – pediera" lang="nso" hreflang="nso" data-title="Nomoro" data-language-autonym="Sesotho sa Leboa" data-language-local-name="pediera" class="interlanguage-link-target"><span>Sesotho sa Leboa</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Nombre" title="Nombre – okzitaniera" lang="oc" hreflang="oc" data-title="Nombre" data-language-autonym="Occitan" data-language-local-name="okzitaniera" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%9D%D1%8B%D0%BC%C3%A6%D1%86" title="Нымæц – osetiera" lang="os" hreflang="os" data-title="Нымæц" data-language-autonym="Ирон" data-language-local-name="osetiera" class="interlanguage-link-target"><span>Ирон</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A9%B0%E0%A8%95" title="ਅੰਕ – punjabera" lang="pa" hreflang="pa" data-title="ਅੰਕ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabera" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczba" title="Liczba – poloniera" lang="pl" hreflang="pl" data-title="Liczba" data-language-autonym="Polski" data-language-local-name="poloniera" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%86%D9%85%D8%A8%D8%B1" title="نمبر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="نمبر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF" title="عدد – paxtunera" lang="ps" hreflang="ps" data-title="عدد" data-language-autonym="پښتو" data-language-local-name="paxtunera" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero" title="Número – portugesa" lang="pt" hreflang="pt" data-title="Número" data-language-autonym="Português" data-language-local-name="portugesa" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Yupay" title="Yupay – kitxua" lang="qu" hreflang="qu" data-title="Yupay" data-language-autonym="Runa Simi" data-language-local-name="kitxua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r" title="Număr – errumaniera" lang="ro" hreflang="ro" data-title="Număr" data-language-autonym="Română" data-language-local-name="errumaniera" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/Numiru" title="Numiru – aromaniera" lang="rup" hreflang="rup" data-title="Numiru" data-language-autonym="Armãneashti" data-language-local-name="aromaniera" class="interlanguage-link-target"><span>Armãneashti</span></a></li><li class="interlanguage-link interwiki-roa-tara mw-list-item"><a href="https://roa-tara.wikipedia.org/wiki/Numere" title="Numere – Tarantino" lang="nap-x-tara" hreflang="nap-x-tara" data-title="Numere" data-language-autonym="Tarandíne" data-language-local-name="Tarantino" class="interlanguage-link-target"><span>Tarandíne</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE" title="Число – errusiera" lang="ru" hreflang="ru" data-title="Число" data-language-autonym="Русский" data-language-local-name="errusiera" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A7%D1%96%D1%81%D0%BB%D0%BE" title="Чісло – Rusyn" lang="rue" hreflang="rue" data-title="Чісло" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%83" title="संख्याः – sanskritoa" lang="sa" hreflang="sa" data-title="संख्याः" data-language-autonym="संस्कृतम्" data-language-local-name="sanskritoa" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%90%D1%85%D1%81%D0%B0%D0%B0%D0%BD" title="Ахсаан – sakhera" lang="sah" hreflang="sah" data-title="Ахсаан" data-language-autonym="Саха тыла" data-language-local-name="sakhera" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/N%C3%B9mmuru" title="Nùmmuru – siziliera" lang="scn" hreflang="scn" data-title="Nùmmuru" data-language-autonym="Sicilianu" data-language-local-name="siziliera" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D9%86%DA%AF" title="انگ – sindhia" lang="sd" hreflang="sd" data-title="انگ" data-language-autonym="سنڌي" data-language-local-name="sindhia" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sg mw-list-item"><a href="https://sg.wikipedia.org/wiki/N%C3%B6m%C3%B6r%C3%B6" title="Nömörö – sangoa" lang="sg" hreflang="sg" data-title="Nömörö" data-language-autonym="Sängö" data-language-local-name="sangoa" class="interlanguage-link-target"><span>Sängö</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Broj" title="Broj – serbokroaziera" lang="sh" hreflang="sh" data-title="Broj" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroaziera" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Am%E1%B8%8Dan" title="Amḍan – tachelhita" lang="shi" hreflang="shi" data-title="Amḍan" data-language-autonym="Taclḥit" data-language-local-name="tachelhita" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Number" title="Number – Simple English" lang="en-simple" hreflang="en-simple" data-title="Number" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C4%8C%C3%ADslo_(matematika)" title="Číslo (matematika) – eslovakiera" lang="sk" hreflang="sk" data-title="Číslo (matematika)" data-language-autonym="Slovenčina" data-language-local-name="eslovakiera" 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/%C5%A0tevilo" title="Število – esloveniera" lang="sl" hreflang="sl" data-title="Število" data-language-autonym="Slovenščina" data-language-local-name="esloveniera" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Nhamba" title="Nhamba – shonera" lang="sn" hreflang="sn" data-title="Nhamba" data-language-autonym="ChiShona" data-language-local-name="shonera" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Thiin_(cillanaad)" title="Thiin (cillanaad) – somaliera" lang="so" hreflang="so" data-title="Thiin (cillanaad)" data-language-autonym="Soomaaliga" data-language-local-name="somaliera" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Numri" title="Numri – albaniera" lang="sq" hreflang="sq" data-title="Numri" data-language-autonym="Shqip" data-language-local-name="albaniera" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D1%80%D0%BE%D1%98" title="Број – serbiera" lang="sr" hreflang="sr" data-title="Број" data-language-autonym="Српски / srpski" data-language-local-name="serbiera" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Wilangan" title="Wilangan – sundanera" lang="su" hreflang="su" data-title="Wilangan" data-language-autonym="Sunda" data-language-local-name="sundanera" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Tal" title="Tal – suediera" lang="sv" hreflang="sv" data-title="Tal" data-language-autonym="Svenska" data-language-local-name="suediera" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Namba" title="Namba – swahilia" lang="sw" hreflang="sw" data-title="Namba" data-language-autonym="Kiswahili" data-language-local-name="swahilia" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/N%C5%AFmera" title="Nůmera – Silesian" lang="szl" hreflang="szl" data-title="Nůmera" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="எண் – tamilera" lang="ta" hreflang="ta" data-title="எண்" data-language-autonym="தமிழ்" data-language-local-name="tamilera" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tcy mw-list-item"><a href="https://tcy.wikipedia.org/wiki/%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B3%86" title="ಸಂಖ್ಯೆ – Tulu" lang="tcy" hreflang="tcy" data-title="ಸಂಖ್ಯೆ" data-language-autonym="ತುಳು" data-language-local-name="Tulu" class="interlanguage-link-target"><span>ತುಳು</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B0%82%E0%B0%96%E0%B1%8D%E0%B0%AF" title="సంఖ్య – telugua" lang="te" hreflang="te" data-title="సంఖ్య" data-language-autonym="తెలుగు" data-language-local-name="telugua" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%B4%D0%B0%D0%B4" title="Адад – tajikera" lang="tg" hreflang="tg" data-title="Адад" data-language-autonym="Тоҷикӣ" data-language-local-name="tajikera" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99" title="จำนวน – thailandiera" lang="th" hreflang="th" data-title="จำนวน" data-language-autonym="ไทย" data-language-local-name="thailandiera" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-ti mw-list-item"><a href="https://ti.wikipedia.org/wiki/%E1%89%81%E1%8C%BD%E1%88%AA" title="ቁጽሪ – tigrinyera" lang="ti" hreflang="ti" data-title="ቁጽሪ" data-language-autonym="ትግርኛ" data-language-local-name="tigrinyera" class="interlanguage-link-target"><span>ትግርኛ</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/San" title="San – turkmenera" lang="tk" hreflang="tk" data-title="San" data-language-autonym="Türkmençe" data-language-local-name="turkmenera" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Bilang" title="Bilang – tagaloa" lang="tl" hreflang="tl" data-title="Bilang" data-language-autonym="Tagalog" data-language-local-name="tagaloa" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Say%C4%B1" title="Sayı – turkiera" lang="tr" hreflang="tr" data-title="Sayı" data-language-autonym="Türkçe" data-language-local-name="turkiera" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Nomboro" title="Nomboro – tsongera" lang="ts" hreflang="ts" data-title="Nomboro" data-language-autonym="Xitsonga" data-language-local-name="tsongera" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BD" title="Сан – tatarera" lang="tt" hreflang="tt" data-title="Сан" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarera" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Chipendero" title="Chipendero – tumbukera" lang="tum" hreflang="tum" data-title="Chipendero" data-language-autonym="ChiTumbuka" data-language-local-name="tumbukera" class="interlanguage-link-target"><span>ChiTumbuka</span></a></li><li class="interlanguage-link interwiki-udm mw-list-item"><a href="https://udm.wikipedia.org/wiki/%D0%9B%D1%8B%D0%B4" title="Лыд – udmurtera" lang="udm" hreflang="udm" data-title="Лыд" data-language-autonym="Удмурт" data-language-local-name="udmurtera" class="interlanguage-link-target"><span>Удмурт</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE" title="Число – ukrainera" lang="uk" hreflang="uk" data-title="Число" data-language-autonym="Українська" data-language-local-name="ukrainera" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF" title="عدد – urdua" lang="ur" hreflang="ur" data-title="عدد" data-language-autonym="اردو" data-language-local-name="urdua" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Son" title="Son – uzbekera" lang="uz" hreflang="uz" data-title="Son" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekera" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/N%C3%B9maro" title="Nùmaro – veneziera" lang="vec" hreflang="vec" data-title="Nùmaro" data-language-autonym="Vèneto" data-language-local-name="veneziera" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Lugu" title="Lugu – Veps" lang="vep" hreflang="vep" data-title="Lugu" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91" title="Số – vietnamera" lang="vi" hreflang="vi" data-title="Số" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamera" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Ihap" title="Ihap – warayera" lang="war" hreflang="war" data-title="Ihap" data-language-autonym="Winaray" data-language-local-name="warayera" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%95%B0" title="数 – wu txinera" lang="wuu" hreflang="wuu" data-title="数" data-language-autonym="吴语" data-language-local-name="wu txinera" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%A2%D0%BE%D0%B9%D0%B3" title="Тойг – kalmykera" lang="xal" hreflang="xal" data-title="Тойг" data-language-autonym="Хальмг" data-language-local-name="kalmykera" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/INANI" title="INANI – xhosera" lang="xh" hreflang="xh" data-title="INANI" data-language-autonym="IsiXhosa" data-language-local-name="xhosera" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%A3" title="რიცხუ – Mingrelian" lang="xmf" hreflang="xmf" data-title="რიცხუ" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A6%D7%90%D7%9C" title="צאל – yiddisha" lang="yi" hreflang="yi" data-title="צאל" data-language-autonym="ייִדיש" data-language-local-name="yiddisha" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/N%E1%BB%8D%CC%81mb%C3%A0" title="Nọ́mbà – jorubera" lang="yo" hreflang="yo" data-title="Nọ́mbà" data-language-autonym="Yorùbá" data-language-local-name="jorubera" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B4%B0%E2%B5%8E%E2%B4%B9%E2%B4%B0%E2%B5%8F" title="ⴰⵎⴹⴰⵏ – amazigera estandarra" lang="zgh" hreflang="zgh" data-title="ⴰⵎⴹⴰⵏ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="amazigera estandarra" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%B0" title="数 – txinera" lang="zh" hreflang="zh" data-title="数" data-language-autonym="中文" data-language-local-name="txinera" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%95%B8" title="數 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="數" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/S%C3%B2%CD%98-ba%CC%8Dk" title="Sò͘-ba̍k – Minnan" lang="nan" hreflang="nan" data-title="Sò͘-ba̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%95%B8" title="數 – kantonera" lang="yue" hreflang="yue" data-title="數" data-language-autonym="粵語" data-language-local-name="kantonera" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Inombolo" title="Inombolo – zuluera" lang="zu" hreflang="zu" data-title="Inombolo" data-language-autonym="IsiZulu" data-language-local-name="zuluera" class="interlanguage-link-target"><span>IsiZulu</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/Q11563#sitelinks-wikipedia" title="Aldatu hizkuntzen arteko loturak" class="wbc-editpage">Aldatu loturak</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="Izen-tarteak"> <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/Zenbaki" title="Eduki orrialdea ikusi [c]" accesskey="c"><span>Artikulua</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Eztabaida:Zenbaki" rel="discussion" title="Artikuluari buruzko eztabaida [t]" accesskey="t"><span>Eztabaida</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="Aldatu hizkuntza aldaera" > <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">euskara</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="Ikusketak"> <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/Zenbaki"><span>Irakurri</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Zenbaki&veaction=edit" title="Orri hau aldatu [v]" accesskey="v"><span>Aldatu</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Zenbaki&action=edit" title="Idatzi orri honen iturburu kodea [e]" accesskey="e"><span>Aldatu iturburu kodea</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Zenbaki&action=history" title="Artikulu honen aurreko bertsioak. [h]" accesskey="h"><span>Ikusi historia</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tresnak" > <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">Tresnak</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">Tresnak</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ezkutatu</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Ekintzak </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/Zenbaki"><span>Irakurri</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Zenbaki&veaction=edit" title="Orri hau aldatu [v]" accesskey="v"><span>Aldatu</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Zenbaki&action=edit" title="Idatzi orri honen iturburu kodea [e]" accesskey="e"><span>Aldatu iturburu kodea</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Zenbaki&action=history"><span>Ikusi historia</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Orokorra </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Berezi:ZerkLotzenDuHona/Zenbaki" title="Orri honetaranzko esteka duten wiki orri guztien zerrenda [j]" accesskey="j"><span>Honanzko esteka duten orriak</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Berezi:RecentChangesLinked/Zenbaki" rel="nofollow" title="Orri honetatik esteka duten orrietako azken aldaketak [k]" accesskey="k"><span>Lotutako orrietako aldaketak</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=eu" title="Irudiak edo media fitxategiak igo [u]" accesskey="u"><span>Fitxategia igo</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Berezi:OrrialdeBereziak" title="Orri berezi guztien zerrenda [q]" accesskey="q"><span>Orri bereziak</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Zenbaki&oldid=9348011" title="Orriaren bertsio honetaranzko esteka iraunkorra"><span>Lotura iraunkorra</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Zenbaki&action=info" title="Orrialde honi buruzko informazio gehiago"><span>Orri honen datuak</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Berezi:CiteThisPage&page=Zenbaki&id=9348011&wpFormIdentifier=titleform" title="Orri honen aipua egiteko moduari buruzko informazioa"><span>Artikulu hau aipatu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Berezi:UrlQ%C4%B1sald%C4%B1c%C4%B1s%C4%B1&url=https%3A%2F%2Feu.wikipedia.org%2Fwiki%2FZenbaki"><span>URL laburra lortu</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Berezi:QrKodu&url=https%3A%2F%2Feu.wikipedia.org%2Fwiki%2FZenbaki"><span>QR kodea jaitsi</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"> Inprimatu/esportatu </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Berezi:Book&bookcmd=book_creator&referer=Zenbaki"><span>Liburu bat sortu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Berezi:DownloadAsPdf&page=Zenbaki&action=show-download-screen"><span>Deskargatu PDF formatuan</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Zenbaki&printable=yes" title="Orrialde honen bertsio inprimagarria [p]" accesskey="p"><span>Inprimatzeko bertsioa</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"> Beste proiektuetan </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/Numbers" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://eu.wikiquote.org/wiki/Zenbaki" hreflang="eu"><span>Wikiesanak</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/Q11563" title="Datuen biltegi elementu batera lotuta [g]" accesskey="g"><span>Wikidata itema</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Itxura"> <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">Itxura</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ezkutatu</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 id="mw-indicator-1-Wikipedia10000" class="mw-indicator"><div class="mw-parser-output"><span typeof="mw:File"><a href="/wiki/Wikipedia:Wikipedia_guztiek_izan_beharreko_artikuluen_zerrenda/3._maila" title="Artikulu hau Wikipedia guztiek izan beharreko artikuluen zerrendaren parte da"><img alt="Artikulu hau Wikipedia guztiek izan beharreko artikuluen zerrendaren parte da" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikipedia-1000.png/20px-Wikipedia-1000.png" decoding="async" width="20" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikipedia-1000.png/30px-Wikipedia-1000.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikipedia-1000.png/40px-Wikipedia-1000.png 2x" data-file-width="1122" data-file-height="1024" /></a></span></div></div> <div id="mw-indicator-2-HezkuntzaPrograma" class="mw-indicator"><div class="mw-parser-output"><span typeof="mw:File"><a href="/wiki/Atari:Hezkuntza" title="Artikulu hau "Kalitatezko 2.000 artikulu 12-16 urteko ikasleentzat" proiektuaren parte da"><img alt="Artikulu hau "Kalitatezko 2.000 artikulu 12-16 urteko ikasleentzat" proiektuaren parte da" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Hezkuntza_Programa_12-16_ikonoa.png/19px-Hezkuntza_Programa_12-16_ikonoa.png" decoding="async" width="19" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Hezkuntza_Programa_12-16_ikonoa.png/28px-Hezkuntza_Programa_12-16_ikonoa.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Hezkuntza_Programa_12-16_ikonoa.png/38px-Hezkuntza_Programa_12-16_ikonoa.png 2x" data-file-width="747" data-file-height="794" /></a></span></div></div> </div> <div id="siteSub" class="noprint">Wikipedia, Entziklopedia askea</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="eu" dir="ltr"><p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_2" poster="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/-bertsomate-_Zenbaki_motak.webm/220px---bertsomate-_Zenbaki_motak.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="113" data-mwtitle="-bertsomate-_Zenbaki_motak.webm" data-mwprovider="wikimediacommons" resource="/wiki/Fitxategi:-bertsomate-_Zenbaki_motak.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7e/-bertsomate-_Zenbaki_motak.webm/-bertsomate-_Zenbaki_motak.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7e/-bertsomate-_Zenbaki_motak.webm/-bertsomate-_Zenbaki_motak.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7e/-bertsomate-_Zenbaki_motak.webm/-bertsomate-_Zenbaki_motak.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/7/7e/-bertsomate-_Zenbaki_motak.webm" type="video/webm; codecs="vp8, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7e/-bertsomate-_Zenbaki_motak.webm/-bertsomate-_Zenbaki_motak.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7e/-bertsomate-_Zenbaki_motak.webm/-bertsomate-_Zenbaki_motak.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7e/-bertsomate-_Zenbaki_motak.webm/-bertsomate-_Zenbaki_motak.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7e/-bertsomate-_Zenbaki_motak.webm/-bertsomate-_Zenbaki_motak.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Zenbaki mota ezberdinak azaltzen dituen bertso sorta.</figcaption></figure> <table style="border: 1px solid #aaa; background-color: #f9f9f9; color: black; margin-bottom: 0.5em; margin-left: 1em; padding: 0.2em; float: right; clear: right; width:25%; text-align:center;"> <tbody><tr style="background:#CCF"> <th><a class="mw-selflink selflink">Zenbakiak</a> <a href="/wiki/Matematika" title="Matematika">matematikan</a> </th></tr> <tr style="background:#E5E5FF"> <th>Zenbaki multzoak </th></tr> <tr> <td><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 \mathbb {N} \subset \mathbb {Z} \subset \mathbb {Q} \subset \mathbb {R} \subset \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mo>⊂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>⊂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mo>⊂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>⊂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} \subset \mathbb {Z} \subset \mathbb {Q} \subset \mathbb {R} \subset \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0579ab35e12fec7fdceb06b0085830426734b946" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.787ex; height:2.509ex;" alt="{\displaystyle \mathbb {N} \subset \mathbb {Z} \subset \mathbb {Q} \subset \mathbb {R} \subset \mathbb {C} }"></span> <p><a href="/wiki/Zenbaki_arrunt" title="Zenbaki arrunt">Zenbaki arruntak</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf9a96b565ea202d0f4322e9195613fb26a9bed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {N} }"></span> <br /> <a href="/wiki/Zenbaki_oso" title="Zenbaki oso">Zenbaki osoak</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle \mathbb {Z} }"></span> <br /> <a href="/wiki/Zenbaki_arrazional" title="Zenbaki arrazional">Zenbaki arrazionalak</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="{\displaystyle \mathbb {Q} }"></span> <br /> <a href="/wiki/Zenbaki_irrazional" title="Zenbaki irrazional">Zenbaki irrazionalak</a> <br /> <a href="/wiki/Zenbaki_erreal" title="Zenbaki erreal">Zenbaki errealak</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {R} }"></span> <br /> <a href="/wiki/Zenbaki_konplexu" title="Zenbaki konplexu">Zenbaki konplexuak</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {C} }"></span> <br /> <a href="/wiki/Zenbaki_aljebraiko" title="Zenbaki aljebraiko">Zenbaki aljebraikoak</a> <br /> <a href="/wiki/Zenbaki_transzendente" title="Zenbaki transzendente">Zenbaki transzendenteak</a> <br /> </p> </td></tr> <tr style="background:#E5E5FF"> <th>Konplexuen hedadurak </th></tr> <tr> <td> <p><a href="/wiki/Koaternioi" title="Koaternioi">Koaternioiak</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {H} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">H</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {H} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e050965453c42bcc6bd544546703c836bdafeac9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \mathbb {H} }"></span> <br /> <a href="/wiki/Oktonioi" title="Oktonioi">Oktonioiak</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {O} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">O</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {O} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1ed2664a4fe515e6fbed25a7193ce663b82920c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \mathbb {O} }"></span><br /> <a href="/w/index.php?title=Zenbaki_hiperkonplexu&action=edit&redlink=1" class="new" title="Zenbaki hiperkonplexu (sortu gabe)">Zenbaki hiperkonplexuak</a> <br /> </p> </td></tr> <tr style="background:#E5E5FF"> <th>Bestelakoak </th></tr> <tr> <td> <p><a href="/wiki/Zenbaki_kardinal" title="Zenbaki kardinal">Zenbaki kardinalak</a> <br /> <a href="/wiki/Zenbaki_ordinal" title="Zenbaki ordinal">Zenbaki ordinalak</a> <br /> <a href="/wiki/Zenbaki_lehen" title="Zenbaki lehen">Zenbaki lehenak</a> <br /> <a href="/wiki/Pi_(zenbakia)" title="Pi (zenbakia)">π</a> = 3.141592654… <br /> <a href="/wiki/E_(zenbakia)" title="E (zenbakia)">e</a> = 2.718281828… <br /> <a href="/wiki/Unitate_irudikari" title="Unitate irudikari">i</a> unitate irudikaria <br /> <a href="/wiki/Infinitu" title="Infinitu">∞</a> infinitua <br /> <a href="/wiki/Urrezko_zenbakia" title="Urrezko zenbakia">Φ</a> = 1,6180339887... <br /> </p> </td></tr> <tr style="background:#E5E5FF"> <th>Zenbaki-sistemak </th></tr> <tr> <td> <p><a href="/wiki/Zenbaki-sistema_hamartar" title="Zenbaki-sistema hamartar">Zenbaki-sistema hamartarra</a> <br /> <a href="/wiki/Zenbaki-sistema_bitar" title="Zenbaki-sistema bitar">Zenbaki-sistema bitarra</a> <br /> <a href="/wiki/Zenbaki-sistema_hamaseitar" title="Zenbaki-sistema hamaseitar">Zenbaki-sistema hamaseitarra</a> <br /> <a href="/wiki/Zenbaki-sistema_zortzitar" title="Zenbaki-sistema zortzitar">Zenbaki-sistema zortzitarra</a> </p> </td></tr></tbody></table> <p><b>Zenbaki</b> bat multzo batek dauzkan unitateen adierazpen matematikoa da.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Zenbaki ezagunenak <a href="/wiki/Zenbaki_arrunt" title="Zenbaki arrunt">arruntak</a> dira (0,1, 2, eta abar), oroar <a href="/wiki/Zenbaketa" title="Zenbaketa">kontatzeko</a>, <a href="/wiki/Neurketa" title="Neurketa">neurtzeko</a> edo <a href="https://en.wikipedia.org/wiki/Nominal_number" class="extiw" title="en:Nominal number">etiketatzeko</a> erabiliak. Bestalde, hainbat orokortze ditugu matematikan: <a href="/wiki/Zenbaki_negatibo" title="Zenbaki negatibo">zenbaki negatiboak</a>, <a href="/wiki/Zenbaki_arrazional" title="Zenbaki arrazional">zenbaki arrazionalak</a> (zatiki bidez adieraz daitezkeenak, adibidez <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 1/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e308a3a46b7fdce07cc09dcab9e8d8f73e37d935" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.487ex; height:2.843ex;" alt="{\displaystyle 1/2}"></span>), <a href="/wiki/Zenbaki_erreal" title="Zenbaki erreal">zenbaki errealak</a> (adibidez <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 {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span> edo <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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span>) eta <a href="/wiki/Zenbaki_konplexu" title="Zenbaki konplexu">zenbaki konplexuak</a> (erro <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 -1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/704fb0427140d054dd267925495e78164fee9aac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.971ex; height:2.343ex;" alt="{\displaystyle -1}"></span> erroa gehituz errealei, hau da, <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 i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> <a href="/wiki/Unitate_irudikari" title="Unitate irudikari">unitate irudikaria</a>). </p><p>Zenbaki indibidualak <a href="/wiki/Ikur" title="Ikur">sinbolo</a> bidez adieraz ditzazkegu, <i>zifrak</i> deituak<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>; adibidez, "2" <a href="/wiki/Bi" title="Bi">bi</a> zenbakia adierazten duen zifra da, baina askotan <i>zenbaki</i> hitza berau erabiltzen da kontzeptua eta sinboloa biak adierazteko. Gainera, sinbolo kopuru finitu bat gogora dezakegunez, gizakiak zifra basikoak ordezkatzeko <a href="/wiki/Zenbaki-sistema" title="Zenbaki-sistema">zenbaki-sistemak</a> ditu. Zenbaki-sistema erabiliena <a href="/wiki/Zenbaki-sistema_hamartar" title="Zenbaki-sistema hamartar">Hindu-Arabiko zenbaki-sistema hamartarra</a> da, non edozein zenbaki 10 zenbaki sinboloren konbinaziez adieraz daitekeen. </p><p>Zenbakiak ikertzen dituen matematikaren adarra <a href="/wiki/Zenbakien_teoria" title="Zenbakien teoria">zenbaki-teoria</a> da , ariketa <a href="/wiki/Aritmetika" title="Aritmetika">aritmetikoetatik</a> at (<a href="/wiki/Gehiketa" class="mw-redirect" title="Gehiketa">batuketa</a>, <a href="/wiki/Kenketa" title="Kenketa">kenketa</a>, <a href="/wiki/Biderketa" title="Biderketa">biderketa</a>, <a href="/wiki/Zatiketa_(matematika)" title="Zatiketa (matematika)">zatiketa</a>, eta <a href="/wiki/Berreketa" title="Berreketa">berreketa</a>) zenbakien teoria modernoak matematikako hainbat adar batzen ditu; hala nola, <a href="/wiki/Analisi_matematiko" title="Analisi matematiko">analisia</a>, <a href="/wiki/Aljebra" title="Aljebra">aljebra</a> edo <a href="/wiki/Geometria" title="Geometria">geometria</a>. Zenbaki-sistema hamartarra baino egitura aljebraiko orokorragoen adibide berezi garrantzitsutat hartzen dira, <a href="/wiki/Eraztun_(matematika)" title="Eraztun (matematika)">eraztunak</a> eta <a href="/wiki/Gorputz_(matematika)" title="Gorputz (matematika)">gorputzak</a> adibidez, eta "<i>zenbaki</i>" hitzak ez du funtsezko esanahirik bertan. </p><p>Erabilera aritmetikoaz gain, zenbakiak askotan errepresentazio ikur moduan erabiltzen dira (mugikor zenbakien kasuan bezala), ordenatzeko (serie-zenbakien kasua online erosketetan), edo kodigo identifikatzaileetan (<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> liburuentzat). Gainera, zenbait zenbakik garrantzi eta esanahi handia dute munduan zehar; adibidez, <a href="/wiki/Hamahiru" title="Hamahiru">13</a> zoritxarreko zenbakia dela uste da mendebaldeko hainbat kulturatan. Gaur egun pseudozientziatzat hartzen den arren, zenbakien esanahi mistikoaren sinesmena, <a href="/wiki/Numerologia" title="Numerologia">numerologia</a> deitua, ohikoa zen mendebaldeko kulturetan. Kondairak dio <a href="/wiki/Eskola_pitagorikoa" title="Eskola pitagorikoa">Pitagorasen jarraitzaileek</a> <a href="/wiki/Hipaso" title="Hipaso">Hipaso</a> greziaz filosofoa hitoarazi zutela erro bi (<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 {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span>) zenbaki irrazionalaren existentzia defendatzeagatik.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Zenbaki_kontzeptuaren_historia">Zenbaki kontzeptuaren historia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=1" title="Aldatu atal hau: «Zenbaki kontzeptuaren historia»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=1" title="Edit section's source code: Zenbaki kontzeptuaren historia"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Kontatzeko_lehen_siboloak">Kontatzeko lehen siboloak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=2" title="Aldatu atal hau: «Kontatzeko lehen siboloak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=2" title="Edit section's source code: Kontatzeko lehen siboloak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbakien sorkuntza historiaurrean kokatzen dela uste da; lehen gizakiaren garaiko objektu fisikoetan (hala nola harriak, hezurrak edo enborrak) hainbat marka aurkitu ditugu, kontatzeko erabiliak seguruenik. Horren lekuko dira <a href="/w/index.php?title=Lebombo&action=edit&redlink=1" class="new" title="Lebombo (sortu gabe)">Lebombo</a>n aurkitu zuten 37.000 urteko antzinatasuna duen babuino-<a href="/w/index.php?title=Hezur_landua&action=edit&redlink=1" class="new" title="Hezur landua (sortu gabe)">hezur landua</a>, 29 hortz markarekin, edo <a href="/wiki/Txekoslovakia" title="Txekoslovakia">Txekoslovakia</a>n aurkitutako otso-hezurra, 5 multzotan banatutako 57 hozkekin. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Huesos_de_ishango.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Huesos_de_ishango.jpg/267px-Huesos_de_ishango.jpg" decoding="async" width="267" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Huesos_de_ishango.jpg/401px-Huesos_de_ishango.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/7/7f/Huesos_de_ishango.jpg 2x" data-file-width="490" data-file-height="224" /></a><figcaption>Ishango-ko hezurra, duela 20.000 urte egindako aztarnak dituena.</figcaption></figure><p> Marka horien erabilerak denboraren jarraipenarekin zerikusirik izan dezakeela iradoki da, adibidez, egunen jarraipena edo kantitateak kontatzeko. Dena dela, markek ez dute posizio-balioaren kontzepturik (egungo zenbaki hamartar sistemak duen bezala); eta honek marken erabilera mugatzen du, zaildu egiten bai du zenbaki handiak irudikatzea. </p><p>Ezagutzen den lehen posizio-baliodun zenbaki sistema <a href="/wiki/Mesopotamia" title="Mesopotamia">Mesopotamiarra</a> zen, 60 oinarrikoa. Marken ordez, sinboloak erabiltzen hasi ziren, zerga- eta jabetza-erregistroak zenbatzeko. Aurkikuntzak Mesopotamian egin ziren, K.a. 8.000. urtean. Hasieran, erregistro horiek zenbatzeko, buztinezko fitxak erabiltzen ziren, baina denbora pasa ahala, buztinezko oholtxoetan hasi ziren idazten zenbakiak, sinbolo desberdinak erabiliz. Hala ere, metodo horiek merkatal edo kontabilitate gaietan bakarrik erabili ziren, nahiz eta lur-neurketan eta astronomian ere oso erabilgarriak izan, esate baterako, mugimendu planetarioak erregistratzeko.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Duela 5.000 urte hasi ziren erabiltzen gaur egun ezagutzen ditugun zenbaki-sinboloak, 10 oinarridunak, <a href="/wiki/Egipto" title="Egipto">Egipton</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Zeroaren_sorkuntza">Zeroaren sorkuntza</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=3" title="Aldatu atal hau: «Zeroaren sorkuntza»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=3" title="Edit section's source code: Zeroaren sorkuntza"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="font-style: italic; padding-left: 2em; margin-bottom: 0.5em;">Sakontzeko, irakurri: «<a href="/wiki/Zero" title="Zero">Zero</a>»</div> <p>Zeroaren erabilera posizionala bere zifra baliotik ezberdindu behar da, bigarrena kontzeptu gisa zenbaki sistema osoa baino berriagoa izanik. Esate baterako, <a href="/wiki/Antzinako_greziar_filosofia" title="Antzinako greziar filosofia">Greziako filosofoek</a> K.a III. mendean, zeroaren egoerarekiko ziurtasun eza adierazi zuten "nola izan daiteke 'ezereza' zerbait?". Hutsunea, ezereza, edo zeroaren izaerak eztabaida filososiko eta erlijioso asko ekarri zituen <a href="/wiki/Erdi_Aroa" title="Erdi Aroa">Erdi Aroan</a> zehar. </p><p>Amerikan, hogei oinarriko zenbaki sistemen lehenengo adierazpena K.a III. mendekoa da. <a href="/wiki/Olmeka" title="Olmeka">Olmeka</a>, <a href="/wiki/Mexiko" title="Mexiko">Mexiko</a> hegoaldeko zibilizazioko biztanleria, hilarri batean zeroaren eta ordenaren kontzeptuak ageri dira. <a href="/wiki/Maien_zibilizazioa" title="Maien zibilizazioa">Maiek</a> (K.a. IV. mendea), aldiz, zeroa adierazteko lau ikur asmatu zituzten. Garrantzitsuenak bi dira: batetik, zero matematikoa adierazteko, barraskilo baten oskolaren ebaketa erabiltzen zen, eta bestetik, egutegiko zeroa adierazteko, lore bat erabiltzen zuten. Dena dela, ez da uste zero honek mundu zaharreko zenbaki-sisteman eraginik izan zuenik. </p><p>Egiazko zero bat zen 525. urteko zenbaki erromatarren tauletan aurkitua ere (<a href="/w/index.php?title=Dionysius_Eziguus&action=edit&redlink=1" class="new" title="Dionysius Eziguus (sortu gabe)">Dionysius Eziguusen</a> eskutik), hitz gisa, <i>nulla</i>, 'ezereza' esan nahi duelarik, ez sinbolo moduan. Zatiketa baten zero hondarra ematen bazuen, <i>nihil</i> erabiltzen zen, 'ezer ez' esan nahi du. </p><p>Zeroaren lehen erabilera aritmetikoa <a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a> indiar <a href="/wiki/Matematikari" title="Matematikari">matematikari</a> eta <a href="/wiki/Astronomo" title="Astronomo">astronomoari</a> dagokio, 628. urtean. Zero zenbaki gisa tratatu eta parte hartzen zuen eragiketak eztabaidatu zituen, zatiketa barne. Garaiko dokumentuek argi adierazten dute kontzeptuak azkar hartu zuela indarra, eta gerora <a href="/wiki/Txina" class="mw-redirect" title="Txina">Txinara</a> eta <a href="https://en.wikipedia.org/wiki/Muslim_world" class="extiw" title="en:Muslim world">mundu islamiarrera</a> zabaldu zela. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbaki_negatiboak">Zenbaki negatiboak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=4" title="Aldatu atal hau: «Zenbaki negatiboak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=4" title="Edit section's source code: Zenbaki negatiboak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbaki negatiboen kontzeptu abstraktua K.a. 100 - K.a. 50 urteen artean sortu zen. <a href="/wiki/Matematika-artearen_bederatzi_kapituluak" title="Matematika-artearen bederatzi kapituluak">Matematika-artearen bederatzi kapituluak</a> (Jiu-Zhang Suanshu) obra matematiko txinatarrak figuren azalerak neurtzeko metodoak biltzen ditu, bertan zenbaki negatiboen ahintzindaria landuz; koefiziente positiboak adierazteko barra gorriak erabiltzen dira, eta koefiziente negatiboak adierazteko beltzak. </p><p>600. hamarkadan, Indian zenbaki negatiboak ohikoak ziren zorrak adierazteko. <a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmaguptak</a>, <a href="/wiki/Bigarren_mailako_ekuazio" title="Bigarren mailako ekuazio">bigarren mailako ekuazioen</a> soluzioetan bi erroak hartu zituen kontuan, nahiz eta horietako bat negatiboa edo irrazionala izan zitekeen. Brahma-Sphuta-Siddhanta (628. urtea) obran, agertu ziren lehenengoz zenbaki positiboen, negatiboen eta zeroaren (+, -, *, /, berreketak eta erroak) <a href="/wiki/Aritmetika" title="Aritmetika">aritmetika</a> sistematizatuta. Zenbaki negatiboak, entitate isolatu bezala ere erabili zituen, <a href="/wiki/Geometria" title="Geometria">geometria</a> aipatu gabe. </p><p>Mendebaldeko lan batean zenbaki negatiboen lehen erreferentzia K.o. III. mendean Grezian datza. <a href="/wiki/Diofanto_Alexandriakoa" title="Diofanto Alexandriakoa">Diofanto Alexandriakoak</a> honako ekuazioa </p> <blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <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 4x+20=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mi>x</mi> <mo>+</mo> <mn>20</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4x+20=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c36f014cee4e54147994ef39de819f5b29f8afe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.918ex; height:2.343ex;" alt="{\displaystyle 4x+20=0}"></span>,</dd></dl> </blockquote> <p>aipatu zuen <a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a> lanean, ekuazio honek emaitza absurdoa emanen zuela esanez. </p><p>Europako matematikari gehienek ez zituzten zenbaki negatiboak onartu XVII. menderarte. Nahiz eta <a href="/wiki/Leonardo_Pisano" title="Leonardo Pisano"> Leonardo Fibonaccik</a> zor gisa interpreta zitezkeen finantza-arazoei irtenbide negatiboak onartu (Liber Abaci-ren 13. kapitulua, 1202), <a href="/w/index.php?title=Nicolas_Chuquet&action=edit&redlink=1" class="new" title="Nicolas Chuquet (sortu gabe)">Nicolas Chuquet</a>, XV. mendea Frantzian, izan zen lehena zenbaki negatiboak erabiltzen. Bere lanean berretzailetzat agertu izan ziren zenbaki negatiboak, baina emaitza hauek zenbaki absurdotzat jo zituen. XVIII. mendean ere, <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> matematikari suizar ezagunak zenbaki negatiboak infinitua baino handiagoak zirela uste zuen, eta ohikoa zen ekuazioren batek emaniko emaitza negatiboa izanez gero hau alde batera uztea, esanguratsuak ez zirelakoan, hau egin izan ohi zuen <a href="/w/index.php?title=Ren%C3%A9_Deskartes&action=edit&redlink=1" class="new" title="René Deskartes (sortu gabe)">René Descartesek</a> ere <a href="/wiki/Koordenatu_kartesiar" title="Koordenatu kartesiar">koordenatu sistema kartesiarreko</a> emaitza negatiboekin. </p> <div class="mw-heading mw-heading3"><h3 id="Zatikiak">Zatikiak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=5" title="Aldatu atal hau: «Zatikiak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=5" title="Edit section's source code: Zatikiak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>1858an <a href="/w/index.php?title=Henry_Rhind&action=edit&redlink=1" class="new" title="Henry Rhind (sortu gabe)">Henry Rhind</a>-ek <a href="/wiki/Egipto" title="Egipto">Egipton</a>, zatikiei buruzko informazioa zeukan papiro bat aurkitu zuen. Papiro hori, K.a. 2.000. eta K.a. 1.800. urteen artekoa da. Hala ere, zatiki unitarioak soilik hartzen zituzten kontuan, hau da, zenbaki naturalen alderantzizkoak zirenak, <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 1/n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0e10667bad240500f5044257143510127e03d69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.72ex; height:2.843ex;" alt="{\displaystyle 1/n}"></span>, eta obalo batekin adierazten zituzten. Bazeuden beste sinbolo bereziekin adierazten zituzten frakzioak, hala nola </p> <blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <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 {2}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc05b5c7c5f0a0020bf8ca7c512314230b1010f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.231ex; height:5.176ex;" alt="{\displaystyle {\frac {2}{n}}}"></span> \textrm{ edo }<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 {n}{n}}+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mi>n</mi> </mfrac> </mrow> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n}{n}}+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/454a6c010ce4c04f79a90e86427c8ae87f5ea5a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.234ex; height:4.676ex;" alt="{\displaystyle {\frac {n}{n}}+1}"></span>,</dd></dl> </blockquote><p> itxurakoak. Papiro honetan, <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 2/n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2/n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fad95ae763b1a6575dece8877b0d8b5967a5365" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.72ex; height:2.843ex;" alt="{\displaystyle 2/n}"></span> motako zenbakien deskonposizio-taulak zeuden, adibidez, </p><blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <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 {2}{5}}={\frac {1}{3}}+{\frac {1}{15}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>15</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2}{5}}={\frac {1}{3}}+{\frac {1}{15}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce217babcff6a011797740811d05e7f0b2768cb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.097ex; height:5.176ex;" alt="{\displaystyle {\frac {2}{5}}={\frac {1}{3}}+{\frac {1}{15}}}"></span> \textrm{ edo } <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 {2}{7}}={\frac {1}{4}}+{\frac {1}{28}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>7</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>28</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2}{7}}={\frac {1}{4}}+{\frac {1}{28}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4bec07b363cf6055db1ae750d7694540abc7d58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.097ex; height:5.343ex;" alt="{\displaystyle {\frac {2}{7}}={\frac {1}{4}}+{\frac {1}{28}}}"></span>.</dd></dl> </blockquote><p> Taula hauetan agertzen ziren frakzioetan erabili zuten <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> zenbakia 1etik 101era bitartekoa zen. </p><p>Zatiki hamartarren kontzeptua oso erlazionatuta dago leku-balio hamartarra duen notazioarekin; biak paraleloan garatu zela dirudi. Adibidez, <a href="/wiki/Jainismo" title="Jainismo">Jain</a> erlijio indiarreko <a href="/wiki/Sutra" title="Sutra">sutra</a> matematikoan (K.a. III. mendea), ohikoa zen <a href="/wiki/Pi" class="mw-redirect" title="Pi">pi</a> edo erro bi (<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 {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span>)-ren hurbilketak kalkulatzea zatiki hamartar bidez. Garai berdintsuan, Babiloniako textu matematikoetan ere 60 oinarriko zenbaki-sistemako zatikiak oso ohikoak ziren. Greziar matematikarietan zatikien analisi zehatzena <a href="/wiki/Euklides" title="Euklides">Euklidesen</a> <i>Elementuak</i> liteke. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbaki_konplexuak">Zenbaki konplexuak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=6" title="Aldatu atal hau: «Zenbaki konplexuak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=6" title="Edit section's source code: Zenbaki konplexuak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbaki konplexuak XVI. mendean agertu ziren matematikari italiarren eskutik, bi eta hirugarren graduko ekuazioak aztertzean. Dena dela, gutxitan onartzen ziren ekuazio hauen soluzio gisa eta ia inoiz ez koefiziente modura, garai hartan zenbaki nebatiboak ere ez baitzeuden oso onartuak. <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartesek</a> zenbaki hauei 'irudikari' izena mespretxuz eman zien, interpretazio errealik ez omen zutelako. </p><p><a href="/wiki/Girolamo_Cardano" title="Girolamo Cardano">Girolamo Cardanok</a> (1501-1576) <i>10 zenbakia bi zatitan zatitu, haien biderkadurak 40 balio dezan</i> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}-10x+40=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>10</mn> <mi>x</mi> <mo>+</mo> <mn>40</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}-10x+40=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfdd81123a3fb67baca2176073a3b876b241ce33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:18.305ex; height:2.843ex;" alt="{\displaystyle x^{2}-10x+40=0}"></span> problema ebaztean, soluzio hauek lortu zituen: <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 5+{\sqrt {-15}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>15</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5+{\sqrt {-15}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47542fd65df12534ec3ebabcad3e9a04fd17bb8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.072ex; height:3.009ex;" alt="{\displaystyle 5+{\sqrt {-15}}}"></span> eta <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 5-{\sqrt {-15}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>15</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5-{\sqrt {-15}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1ba528b9eefa844a719e335df01be4c1c43669a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.072ex; height:3.009ex;" alt="{\displaystyle 5-{\sqrt {-15}}}"></span>. Ekuazio kubikoak Cardano-Tartaglia formularen bidez ebaztean, nahiz eta emaitzak errealak izan, zenbaki negatiboen erroak ageri dira tarteko urratsetan. Egoera horretan, <a href="/w/index.php?title=Rafael_bombelli&action=edit&redlink=1" class="new" title="Rafael bombelli (sortu gabe)">Rafael Bombellik</a> (1526-1573) bere <i>Aljebra</i> liburuan 'ideia ero' zeritzona izan zuela dio, hau da, errotzaileek errokizunen erlazio bera izan eta haiekin lan egin zezaketen, beranduago, desagerrarazten saiatuz gero. </p><p>Beste nahasmen iturrietako bat zenbaki konplexuen erabilera aljebraikoak sorturiko arazoak ziren. Adibidez, </p> <blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <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 ({\sqrt {-1}})^{2}={\sqrt {-1}}{\sqrt {-1}}=-1,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\sqrt {-1}})^{2}={\sqrt {-1}}{\sqrt {-1}}=-1,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a0b671e45699df4863310922bc967c0262ee97e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.397ex; height:3.176ex;" alt="{\displaystyle ({\sqrt {-1}})^{2}={\sqrt {-1}}{\sqrt {-1}}=-1,}"></span></dd></dl> </blockquote> <p>ez zetorren bat zenbaki positiboen identitate aljebraikoarekin </p> <blockquote style="padding: 5px 10px;background-color: white; color:black; text-align:left; margin-left:30px; margin-bottom:0.4em; margin-top:0.2em; min-width:50%;"> <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 {\sqrt {a}}{\sqrt {b}}={\sqrt {ab}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>a</mi> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>b</mi> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>a</mi> <mi>b</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {a}}{\sqrt {b}}={\sqrt {ab}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43a6fe99883dd2ee2bda43eab716e18d9bece3a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.361ex; height:3.343ex;" alt="{\displaystyle {\sqrt {a}}{\sqrt {b}}={\sqrt {ab}}}"></span>.</dd></dl> </blockquote> <p>Gaur egun badakigu ekuazio hau ez dela betetzen zenbaki konplexuentzako, eta zailtasun hau izan zen <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> zenbaki irudikarientzako sinbolo berri bat sortzera eraman zuena <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 i={\sqrt {-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i={\sqrt {-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/370c8cebe9634fbfc84c29ea61680b0ad4a1ae0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.807ex; height:3.009ex;" alt="{\displaystyle i={\sqrt {-1}}}"></span>. </p><p>Zenbaki konplexuen irudikapen grafikoa <a href="/wiki/Caspar_Wessel" title="Caspar Wessel">Caspar Wesselek</a> (1745-1818) egin zuen, baina oharkabean igaro zen. Horregaitik deitzen zaio zenbaki konplexuen planoari <i>Gaussen planoa</i>, <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gaussi</a> (1777-1855) esleitzen baitzaio. <a href="/w/index.php?title=Girard&action=edit&redlink=1" class="new" title="Girard (sortu gabe)">Girarden</a> garaitik (XVII. mendearen erditik) ezagutzen da zenbaki errealak zuzen baten puntuekin bat egiten dutela, beraz hauek ardatz bertikalean kokatuz gero, zenbaki konplexuak bi dimentsioko plano batean irudika ditzakegu, non irudikariak ardatz bertikalean kokatzen diren. <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+bi}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a+bi}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a92f853c2c9235c06be640b91b7c75e2a907cbda" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.87ex; height:2.343ex;" alt="{\displaystyle a+bi}"></span> motako zenbaki konplexuekin ere lan egin zuen, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> eta <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 b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> zenbaki osoak izanik, eta <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 i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> Eulerren zenbaki irudikarien ikurra. Gaussek zabaldu zuen honen erabilera <i>Disquisitiones arithmeticae</i> obran (1801). </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:A_plus_bi.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/A_plus_bi.svg/250px-A_plus_bi.svg.png" decoding="async" width="250" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/A_plus_bi.svg/375px-A_plus_bi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/A_plus_bi.svg/500px-A_plus_bi.svg.png 2x" data-file-width="182" data-file-height="122" /></a><figcaption>Zenbaki konplexuak <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 z=a+ib}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>i</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z=a+ib}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/768804bf1e5f2b40378497f93bb04a10ce64098b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.057ex; height:2.343ex;" alt="{\displaystyle z=a+ib}"></span> bi dimentsioko planu konplexuko bikote moduan adieraz daitezke <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,b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a,b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e5710198f33b00695903460983021e75860e2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.071ex; height:2.843ex;" alt="{\displaystyle (a,b)}"></span>. <i>Re</i> ardatz horizontal erreala da eta <i>Im</i> ardatz bertikal irudikaria, non <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 i^{2}=-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i^{2}=-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88e98a401d352e5037d5043028e2d7f449e83fa6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.926ex; height:2.843ex;" alt="{\displaystyle i^{2}=-1}"></span>.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Indukzio_matematikoaren_printzipioa">Indukzio matematikoaren printzipioa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=7" title="Aldatu atal hau: «Indukzio matematikoaren printzipioa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=7" title="Edit section's source code: Indukzio matematikoaren printzipioa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Indukzio matematikoaren aurrekaria indukzio osoa izeneko frogapen metodoa da. <a href="/wiki/Pascal" class="mw-disambig" title="Pascal">Pascal</a>ek (1623-1662) indukzio matematikoaren metodoa erabili zuen, gaur egun ezagutzen dugun moduan, bere izena daraman zenbaki triangeluari dagozkion propietateak frogatzeko. Indukzioaren bidezko frogapenek bi zati dituzte beti: oinarrizko urratsa eta indukziozko urratsa. Ondoren, notazio gaurkotuan deskribatzen dira: </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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> zenbaki arrunten azpimultzoa bada (<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 \aleph }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">ℵ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/306c55e6bc96d94db729ff5821c8f45a34c72bce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.42ex; height:2.176ex;" alt="{\displaystyle \aleph }"></span> moduan ezaguna) eta <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> elementu bakoitzak <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 P(n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e303d2c14cd399b6f52b468c9fd44a542bed422" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.949ex; height:2.843ex;" alt="{\displaystyle P(n)}"></span> propietatea betetzen badu non: </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span> <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> azpimultzoan dago.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> -n badago, orduan <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 n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a135e65a42f2d73cccbfc4569523996ca0036f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n+1}"></span> ere <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> -n dago.</li></ol> <p>Beraz, <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>=<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 \aleph }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">ℵ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/306c55e6bc96d94db729ff5821c8f45a34c72bce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.42ex; height:2.176ex;" alt="{\displaystyle \aleph }"></span>, hau da, edozein <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> zenbaki arruntak <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 P(n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e303d2c14cd399b6f52b468c9fd44a542bed422" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.949ex; height:2.843ex;" alt="{\displaystyle P(n)}"></span> propietatea betetzen du. </p><p>Intuizioz, indukzioa domino efektu gisa ulertzen da. Domino fitxen errenkada infinitua dugula suposatuz, oinarrizko urratsa lehenengo fitxa jaurtitzean datza; bestalde, urrats induktiboak frogatzen du fitxaren bat erortzen bada, hurrengo fitxa ere eroriko dela. Horren ondorioa errenkada horretako fitxa guztiak bota daitezkeela da. </p> <div class="mw-heading mw-heading3"><h3 id="Multzoen-teoria">Multzoen-teoria</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=8" title="Aldatu atal hau: «Multzoen-teoria»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=8" title="Edit section's source code: Multzoen-teoria"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Multzoen teoriak zenbaki arruntak eta zenbaki errealak zenbaki konplexuek zenbaki errealen multzora hedatzen zituzten modu ezberdinez zabaltzeko modu asko eta askotarikoak iradoki zituen. Multzoaren ideia elementu-kopuru ez finitu batekin atzemateko saiakerak zenbaki transfinituen aritmetikara eraman zuen, zenbaki naturalak orokortzen baitituzte, baina ez zenbaki osoak. Zenbaki transfinituak <a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a>rek sartu zituen 1873 inguruan. </p><p>Analisi ez-estandarrean erabilitako zenbaki hipererrealek zenbaki errealak orokortzen dituzte, baina ez zenbaki konplexuak (nahiz eta konplexutasun bat onartzen duten, zenbaki konplexuak ere orokortuko lituzkeena). Zenbaki hipererrealak dirudien arren, ez dute emaitza matematiko interesgarririk ematen analisi errealean lor daitezkeenetatik haratago doazenik, frogapen eta froga matematiko batzuek sinpleagoak dirudite zenbaki hipererrealen formalismoan, eta, beraz, ez daude garrantzi praktikotik salbuetsita. </p> <div class="mw-heading mw-heading3"><h3 id="Irrazionalen_teoriak">Irrazionalen teoriak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=9" title="Aldatu atal hau: «Irrazionalen teoriak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=9" title="Edit section's source code: Irrazionalen teoriak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>XIX. mendearen erdialdera arte matematikariak zenbakien ulermen intuitiboarekin konformatzen ziren eta euren propietate sinpleak ez ziren logikoki XIX. mendera arte ezarriak izan. Azterketan zorroztasuna sartzeak agerian utzi zuen zenbaki errealen sistemaren argitasunik eza eta zehaztasunik eza, eta oinarri aritmetikoen gainean egituratze logikoa eskatzen zuen. </p><p><a href="/wiki/Bernard_Bolzano" title="Bernard Bolzano">Bolzano</a>k zenbaki errealak zenbaki arrazionalen segidetan oinarrituta eraikitzeko saiakera bat egin zuen, baina bere teoria oharkabean igaro zen eta 1962ra arte ez zen argitaratu. <a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">Hamiltonek</a> saiakera bat egin zuen, denbora magnitudeari erreferentzia eginez, zenbaki arrazionalen banaketetatik abiatuta: </p> <dl><dd>baldin eta <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={\cfrac {n_{1}}{m_{1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\cfrac {n_{1}}{m_{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/329b121a083297f09ca575cc57b305020c745aed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:8.259ex; height:7.176ex;" alt="{\displaystyle a={\cfrac {n_{1}}{m_{1}}}}"></span>, <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 b={\cfrac {n_{1}^{2}}{m_{1}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\cfrac {n_{1}^{2}}{m_{1}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6e1d987facc4446ab44a17401e6d780549b153b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:8.027ex; height:7.176ex;" alt="{\displaystyle b={\cfrac {n_{1}^{2}}{m_{1}^{2}}}}"></span> denean eta baldin eta <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={\cfrac {n_{2}}{m_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\cfrac {n_{2}}{m_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f51ecbb4c00d8a61cfdae6875037c04fb1d4d61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:8.259ex; height:7.176ex;" alt="{\displaystyle a={\cfrac {n_{2}}{m_{2}}}}"></span>, <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 b={\cfrac {n_{2}^{2}}{m_{2}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\cfrac {n_{2}^{2}}{m_{2}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c21e4ebee7d4de729ddb37b34748a7d759adf480" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:8.027ex; height:7.176ex;" alt="{\displaystyle b={\cfrac {n_{2}^{2}}{m_{2}^{2}}}}"></span> denean <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 \quad \longrightarrow \quad a={\sqrt {b}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="1em" /> <mo stretchy="false">⟶</mo> <mspace width="1em" /> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>b</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \quad \longrightarrow \quad a={\sqrt {b}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/273ce844340bb90ddf036838748a87524bd222c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.358ex; height:3.009ex;" alt="{\displaystyle \quad \longrightarrow \quad a={\sqrt {b}}}"></span></dd> <dd>Baina ez zuen bere teoria gehiago garatu.</dd> <dd>Baina 1872an bertan bost matematikarik, frantses batek eta lau alemanek, zenbaki errealen aritmetizazioari buruzko beren lanak argitaratu zituzten</dd></dl> <ul><li><a href="/w/index.php?title=Charles_Merayk&action=edit&redlink=1" class="new" title="Charles Merayk (sortu gabe)">Charles Merayk</a> (1835-1911) Nouveau précis d 'analyse infinitesimale lanean zenbaki irrazionala zenbaki arrazionalen segiden limite gisa definitzen du, kontuan hartu gabe limitearen existentziak berak zenbaki errealaren definizioa suposatzen duela.</li></ul> <ul><li>Hermann Heinek (1821-1881), Journal de Crelle egunkarian, 1872an, «Funtzioen teoriaren elementuak» izeneko artikulua argitaratu zuen, non <a href="/w/index.php?title=Cantor&action=edit&redlink=1" class="new" title="Cantor (sortu gabe)">Cantor</a>ren antzeko ideiak proposatzen zituen, gaur egun «<a href="/w/index.php?title=Teorema_de_Heine-Cantor&action=edit&redlink=1" class="new" title="Teorema de Heine-Cantor (sortu gabe)">Heine-Cantorren teorema</a>» deitzen dena.</li></ul> <ul><li><a href="/wiki/Richard_Dedekind" title="Richard Dedekind">Richard Dedekindek</a> (1831-1916) <a href="/w/index.php?title=Stetigkeit_und_irrationale_zahlen&action=edit&redlink=1" class="new" title="Stetigkeit und irrationale zahlen (sortu gabe)">Stetigkeit und irrationale zahlen</a> argitaratu zuen. Bere ideia zuzen errealaren jarraitutasunean eta zenbaki arrazionalak bakarrik kontuan hartuz dauden "zuloetan" oinarritzen da. «R domeinua» izeneko atalean, zuzenaren jarraitutasuna ezartzen duen axioma bat adierazten du: «Zuzenaren puntu bakoitzak zuzenaren puntuak bi motatan banatzen ditu, hots, lehenengoaren puntu bakoitza bigarren motako puntu bakoitzaren ezkerraldean dago; orduan, zatiketa hori eragiten duen puntu bakarra dago». Ideia hori bera erabiltzen du «zenbaki irrazionalen sorrera» atalean, «Ebakidura» kontzeptua sartzeko. <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a>ek gero esango luke klase batekin nahikoa dela, honek bestea definitzen baitu.</li></ul> <ul><li><a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a> (1845-1918). Oinarrizko segida, segida elementala eta oinarrizko segidaren limite kontzeptuak definitzen ditu, eta horietatik abiatuz zenbaki erreala definitzen du.</li></ul> <ul><li><a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a> (1815-1897). Ez zuen bere lana argitaratu, Bolzano, Abel eta Cauchykoen jarraipena, baina Berlingo Unibertsitatean ikasi zuelako izan zen ezaguna. «Tarte ahokatuetan» oinarritutako karakterizazioa, zenbaki arrazional bati kontrajar dakizkiokeenak baina ez derrigorrez egiten dutenak, ez da aurrekoak bezain orokorgarria, baina zenbaki errealen irudikapen hamartarrerako sarbide erraza ematen du.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Aljebra_hiperkonplexuak">Aljebra hiperkonplexuak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=10" title="Aldatu atal hau: «Aljebra hiperkonplexuak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=10" title="Edit section's source code: Aljebra hiperkonplexuak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbaki errealetatik zenbaki konplexuak lortzeko eraikuntzak eta horiek planoko antzeko transformazioen multzoarekin duten loturak <a href="/w/index.php?title=N%C3%BAmeros_hipercomplejos&action=edit&redlink=1" class="new" title="Números hipercomplejos (sortu gabe)">zenbaki hiperkonplexuak</a> izenez ezagutzen diren antzeko beste orokortze batzuk iradoki zizkien matematikari batzuei. Orokortze horietan guztietan zenbaki konplexuak zenbaki-sistema berri horien azpimultzo bat dira, nahiz eta orokortze horiek aljebra-egitura matematikoa izan gorputz baten gainean, baina haietan biderkatze-eragiketa ez da kommutatiboa. </p> <div class="mw-heading mw-heading2"><h2 id="Zenbakien_sailkapena">Zenbakien sailkapena</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=11" title="Aldatu atal hau: «Zenbakien sailkapena»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=11" title="Edit section's source code: Zenbakien sailkapena"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Zenbaki_arruntak">Zenbaki arruntak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=12" title="Aldatu atal hau: «Zenbaki arruntak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=12" title="Edit section's source code: Zenbaki arruntak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="font-style: italic; padding-left: 2em; margin-bottom: 0.5em;">Sakontzeko, irakurri: «<a href="/wiki/Zenbaki_arrunt" title="Zenbaki arrunt">Zenbaki arrunt</a>»</div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><span><video id="mwe_player_3" poster="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/-bertsomate-_Zenbaki_arruntak.webm/220px---bertsomate-_Zenbaki_arruntak.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="32" data-mwtitle="-bertsomate-_Zenbaki_arruntak.webm" data-mwprovider="wikimediacommons" resource="/wiki/Fitxategi:-bertsomate-_Zenbaki_arruntak.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/88/-bertsomate-_Zenbaki_arruntak.webm/-bertsomate-_Zenbaki_arruntak.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/88/-bertsomate-_Zenbaki_arruntak.webm/-bertsomate-_Zenbaki_arruntak.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/88/-bertsomate-_Zenbaki_arruntak.webm/-bertsomate-_Zenbaki_arruntak.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/8/88/-bertsomate-_Zenbaki_arruntak.webm" type="video/webm; codecs="vp8, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/88/-bertsomate-_Zenbaki_arruntak.webm/-bertsomate-_Zenbaki_arruntak.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/88/-bertsomate-_Zenbaki_arruntak.webm/-bertsomate-_Zenbaki_arruntak.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/88/-bertsomate-_Zenbaki_arruntak.webm/-bertsomate-_Zenbaki_arruntak.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/8/88/-bertsomate-_Zenbaki_arruntak.webm/-bertsomate-_Zenbaki_arruntak.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>0,1,2,3,4 / ta osteko denak / izenak dion gisan / dira ARRUNTenak / duguna zenbatzeko / balio dutenak.</figcaption></figure> <p>Zenbaki motarik ezagunenan <a href="/wiki/Zenbaki_arrunt" title="Zenbaki arrunt">zenbaki arruntak</a> dira, askotan <b>zenbaki oso</b> ere deituak: <a href="/wiki/Bat" title="Bat">1</a>, <a href="/wiki/Bi" title="Bi">2</a>, <a href="/wiki/Hiru" title="Hiru">3</a> eta ondoren doazen guztiak. Tradizionalki zerrenda hau 1 zenbakiarekin hasi da, <a href="/wiki/Zero" title="Zero">0</a> ez baitzen kontsideratzen zenbaki bat <a href="/wiki/Antzinako_Grezia" title="Antzinako Grezia">Antzinako Grezian</a>. Hala ere, <a href="/wiki/XIX._mende" class="mw-redirect" title="XIX. mende">XIX. mendetik</a> aurrera <a href="/wiki/Multzo-teoria" title="Multzo-teoria">multzo-teoriaren</a> garatzaileek eta matematikariek 0 gehitzen hasi ziren zenbaki arrunte barnean. Gaur egun, matematikariek bi multzoak izendatzeko erabiltzen dute zenbaki arruntak, 0 barnebildu edo ez<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>. Matematikan zenbaki hauek izendatzeko erabiltzen den sinboloa <b>N</b> da, baita <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 \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf9a96b565ea202d0f4322e9195613fb26a9bed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {N} }"></span> idatzia, eta batzuetan <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 \mathbb {N} _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77ab7e98123f0def29a1cd3df96a0b7a58f4202c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \mathbb {N} _{0}}"></span> edo <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 \mathbb {N} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cca915d54ae835781191ae19599e11c7ff3d066" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \mathbb {N} _{1}}"></span> beharrezkoa denean adieraztea 0 edo 1 zenbakitik hasten diren. </p><p><a href="/wiki/Zenbaki_sistema_hamartar" class="mw-redirect" title="Zenbaki sistema hamartar">Zenbaki sistema hamartarrean</a>, gaur egun operazio matematikoetan ia unibertsalki erabiltzen dena, zenbaki naturalak hamar <a href="/wiki/Digitu" class="mw-redirect" title="Digitu">digitu</a> erabiltzen idazten dira: 0, 1, 2, 3, 4, 5, 6, 7, 8, eta 9. <a href="/w/index.php?title=Zenbaki-sistemaren_oinarri&action=edit&redlink=1" class="new" title="Zenbaki-sistemaren oinarri (sortu gabe)">Zenbaki-sistemaren oinarria</a> zenbaki-sistema batek zenbakiak errepresentatzeko erabiltzen duen digito ezberdinen kopurua da. Zenbaki sistema hamartarrean 10 da<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>. Sistema honetan, eskuman idazten den sistemak 1-eko leku-balioa du, eta beste edozein digitok bere eskubian dagoen digitoaren 10 aldiz balio handiagoa izango du. Adibidez, 34 zenbakian <i>4</i> digitoak <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 4\times 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mo>×</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4\times 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f994e262c8d0c841800b3983d056431faa3554b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.165ex; height:2.176ex;" alt="{\displaystyle 4\times 1}"></span> balioa izango du eta <i>3</i> digitoak <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3\times 10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>×</mo> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\times 10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfce0394d4e8461c1d53aaf47798fce4d549a809" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.328ex; height:2.176ex;" alt="{\displaystyle 3\times 10}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbaki_osoak">Zenbaki osoak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=13" title="Aldatu atal hau: «Zenbaki osoak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=13" title="Edit section's source code: Zenbaki osoak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="font-style: italic; padding-left: 2em; margin-bottom: 0.5em;">Sakontzeko, irakurri: «<a href="/wiki/Zenbaki_oso" title="Zenbaki oso">Zenbaki oso</a>»</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_4" poster="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/-bertsomate-_Zenbaki_osoak.webm/220px---bertsomate-_Zenbaki_osoak.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="30" data-mwtitle="-bertsomate-_Zenbaki_osoak.webm" data-mwprovider="wikimediacommons" resource="/wiki/Fitxategi:-bertsomate-_Zenbaki_osoak.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/-bertsomate-_Zenbaki_osoak.webm/-bertsomate-_Zenbaki_osoak.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/-bertsomate-_Zenbaki_osoak.webm/-bertsomate-_Zenbaki_osoak.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/-bertsomate-_Zenbaki_osoak.webm/-bertsomate-_Zenbaki_osoak.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/e/e2/-bertsomate-_Zenbaki_osoak.webm" type="video/webm; codecs="vp8, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/-bertsomate-_Zenbaki_osoak.webm/-bertsomate-_Zenbaki_osoak.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/-bertsomate-_Zenbaki_osoak.webm/-bertsomate-_Zenbaki_osoak.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/-bertsomate-_Zenbaki_osoak.webm/-bertsomate-_Zenbaki_osoak.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e2/-bertsomate-_Zenbaki_osoak.webm/-bertsomate-_Zenbaki_osoak.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Jasotzeko adina / dugunez kentzeko / minus-a beharrezko zen / hori azaltzeko / negatiboak / gehitu / ziren OSOtzeko</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_5" poster="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Zenbaki_osoak_Azalpena_1_DBH.webm/220px--Zenbaki_osoak_Azalpena_1_DBH.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="268" data-mwtitle="Zenbaki_osoak_Azalpena_1_DBH.webm" data-mwprovider="wikimediacommons" resource="/wiki/Fitxategi:Zenbaki_osoak_Azalpena_1_DBH.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/Zenbaki_osoak_Azalpena_1_DBH.webm/Zenbaki_osoak_Azalpena_1_DBH.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/Zenbaki_osoak_Azalpena_1_DBH.webm/Zenbaki_osoak_Azalpena_1_DBH.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/Zenbaki_osoak_Azalpena_1_DBH.webm/Zenbaki_osoak_Azalpena_1_DBH.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/d/d0/Zenbaki_osoak_Azalpena_1_DBH.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/Zenbaki_osoak_Azalpena_1_DBH.webm/Zenbaki_osoak_Azalpena_1_DBH.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/Zenbaki_osoak_Azalpena_1_DBH.webm/Zenbaki_osoak_Azalpena_1_DBH.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d0/Zenbaki_osoak_Azalpena_1_DBH.webm/Zenbaki_osoak_Azalpena_1_DBH.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption><b>Zenbaki osoak</b> ulertzeko bideoa.<hr /><span style="color: #777;"><figure class="mw-halign-left" typeof="mw:File"><a href="https://www.jakindun.com/" rel="nofollow"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/33px-Jakindun_logoa.png" decoding="async" width="33" height="33" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/50px-Jakindun_logoa.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/66px-Jakindun_logoa.png 2x" data-file-width="225" data-file-height="225" /></a><figcaption></figcaption></figure>Bideo hau Jakindun elkarteak egin du. Gehiago dituzu eskuragarri <a rel="nofollow" class="external text" href="https://www.jakindun.com/">euren gunean</a>. Bideoak dituzten artikulu guztiak ikus ditzakezu <a href="/wiki/Kategoria:Jakindunen_bideoak_dituzten_artikuluak" title="Kategoria:Jakindunen bideoak dituzten artikuluak"><b>hemen</b></a>.</span></figcaption></figure> <p><a href="/wiki/Zenbaki_oso" title="Zenbaki oso">Zenbaki osoen</a> multzoan <a href="/wiki/Zenbaki_arrunt" title="Zenbaki arrunt">zenbaki arruntak</a> biltzen dira (0,1,2,...), beren aurkakoekin batera (-0,-1,-2,...). -0 eta 0 berdintzat jotzen dira. Zenbaki osoen multzoa Z hizkiaz izendatu ohi da (<i>Zahlen</i> germanierazko hitzetik). Zenbaki osoak batu, kendu eta biderkatu egin daitezke: emaitza beti izango da zenbaki oso bat. </p><p>x+a=b motako ekuazioen soluzioa, non a eta b zenbaki osoak diren, zenbaki osoa izango da. <a href="/wiki/Zenbaki_arrunt" title="Zenbaki arrunt">Zenbaki arrunten</a> kasuan ez da esaterako gauza bera gertatzen. Zorrotzago, zenbaki osoen multzoak, batuketa eta biderketa eragiketak definitu ondoren, <a href="/wiki/Eraztun_trukakorra" class="mw-redirect" title="Eraztun trukakorra">eraztun trukakorra</a> osatzen duela esan behar da. </p><p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Zenbaki_arrazionalak">Zenbaki arrazionalak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=14" title="Aldatu atal hau: «Zenbaki arrazionalak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=14" title="Edit section's source code: Zenbaki arrazionalak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="font-style: italic; padding-left: 2em; margin-bottom: 0.5em;">Sakontzeko, irakurri: «<a href="/wiki/Zenbaki_arrazional" title="Zenbaki arrazional">Zenbaki arrazional</a>»</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_6" poster="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/-bertsomate-_zenbaki_arrazionalak.webm/220px---bertsomate-_zenbaki_arrazionalak.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="29" data-mwtitle="-bertsomate-_zenbaki_arrazionalak.webm" data-mwprovider="wikimediacommons" resource="/wiki/Fitxategi:-bertsomate-_zenbaki_arrazionalak.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/-bertsomate-_zenbaki_arrazionalak.webm/-bertsomate-_zenbaki_arrazionalak.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/-bertsomate-_zenbaki_arrazionalak.webm/-bertsomate-_zenbaki_arrazionalak.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/-bertsomate-_zenbaki_arrazionalak.webm/-bertsomate-_zenbaki_arrazionalak.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/a/ae/-bertsomate-_zenbaki_arrazionalak.webm" type="video/webm; codecs="vp8, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/-bertsomate-_zenbaki_arrazionalak.webm/-bertsomate-_zenbaki_arrazionalak.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/-bertsomate-_zenbaki_arrazionalak.webm/-bertsomate-_zenbaki_arrazionalak.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/-bertsomate-_zenbaki_arrazionalak.webm/-bertsomate-_zenbaki_arrazionalak.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/-bertsomate-_zenbaki_arrazionalak.webm/-bertsomate-_zenbaki_arrazionalak.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Ta elkarbanatzea / denez naturala / pizza bat zein pastel bat / zatitu bezala / osoen zatidura / da ARRAZIONALA</poem></figcaption></figure> <p><a href="/wiki/Zenbaki_arrazional" title="Zenbaki arrazional">Zenbaki arrazional</a> bat <a href="/wiki/Zatiki" class="mw-redirect" title="Zatiki">zatiki</a> moduan espresa daitekeen edozein zenbaki da, <a href="/w/index.php?title=Zenbakitzaile&action=edit&redlink=1" class="new" title="Zenbakitzaile (sortu gabe)">zenbakitzailea</a> <a href="/wiki/Zenbaki_oso" title="Zenbaki oso">zenbaki oso</a> bat baldin bada eta <a href="/w/index.php?title=Izendatzaile&action=edit&redlink=1" class="new" title="Izendatzaile (sortu gabe)">izendatzailea</a> zenbaki oso positibo bat. Izendatzaile negatiboak baimentzen dira, baina normalki ez dira erabiltzen, edozein zenbaki arrazional izendatzaile positibo bat duen zatiki baten berdina delako. Zatikiak bi zenbaki osorekin osatzen dira, zenbakitzailea eta izendatzailea, barra bat jarrita zatitzen euren erdia. Adibidez <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 {\tfrac {m}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>m</mi> <mi>n</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {m}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1413d4c83a94e754258e428fcd72d4fc6bcc2e3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.279ex; height:3.009ex;" alt="{\displaystyle {\tfrac {m}{n}}}"></span> zatikiak <i>m</i> zatitzen du <i>n</i> atal berdinetan. Bi zatiki egon daitezke zenbaki arrazional berdinari dagokionak, adibidez <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 {\tfrac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edef8290613648790a8ac1a95c2fb7c3972aea2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.658ex; height:3.509ex;" alt="{\displaystyle {\tfrac {1}{2}}}"></span> eta <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 {\tfrac {2}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>2</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7ae6a7bf3fa207ef6bdbabc22404a3d0abb6c47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.658ex; height:3.509ex;" alt="{\displaystyle {\tfrac {2}{4}}}"></span> berdinak dira, hau da, </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 {1 \over 2}={2 \over 4}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>4</mn> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1 \over 2}={2 \over 4}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50b6a5243bcf697d6f4e39f8102e66e3888269b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.742ex; height:5.176ex;" alt="{\displaystyle {1 \over 2}={2 \over 4}.}"></span></dd></dl> <p>Oorkorrean </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 \over b}={c \over d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>d</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {a \over b}={c \over d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f0696d2d2f38d22a180747bc53adbd900b638ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.216ex; height:4.843ex;" alt="{\displaystyle {a \over b}={c \over d}}"></span> baldin eta bakarrik <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\times d}={c\times b}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mo>×</mo> <mi>d</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>×</mo> <mi>b</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {a\times d}={c\times b}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b3fe0d5559d25ae52e0661aa99eee495c1554a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.876ex; height:2.176ex;" alt="{\displaystyle {a\times d}={c\times b}.}"></span></dd></dl> <p><i>m</i>ren <a href="/wiki/Balio_absolutu" title="Balio absolutu">balio absolutua</a> <i>n</i>rena baino handiagoa bada (positiboak direla pentsatuz), orduan zatikiaren balio absolutua 1 baino handiago izango da. Zatikiak izna daitezke 1 baino handiago, txikiago edo berdin, eta izan daitezke positibo, negatibo edo 0. Zenbaki arrazional guztien multzoak zenbaki oso guztiak barnean hartzen ditu, edozein zenbaki oso idatzi daitekeelako izendatzailearen zatiki gisa. Adibidez, -7 idatzi daiteke <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 {\tfrac {-7}{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mo>−</mo> <mn>7</mn> </mrow> <mn>1</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {-7}{1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d814393c20097c5886a0d769f6bdf202aabf431f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.937ex; height:3.676ex;" alt="{\displaystyle {\tfrac {-7}{1}}}"></span> gisa. Zenbaki arrazionalen ikurra <b>Q</b> da (<i>quotient</i> hitzetik), eta horrela ere idatzi daiteke: <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 \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="{\displaystyle \mathbb {Q} }"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbaki_arrunt_bereziak">Zenbaki arrunt bereziak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=15" title="Aldatu atal hau: «Zenbaki arrunt bereziak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=15" title="Edit section's source code: Zenbaki arrunt bereziak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbakien ezaugarrien ikerketari esker, bitxiak diren zenbakiak aurkitu dira, matematikoki balio berezirik izan ez arren: </p> <ul><li><b>Sheldon,</b> adibidez, 73 zenbakia. 21. zenbaki lehena da, eta 7 · 3 = 21 betetzen da. Digituak trukatzean, 37 zenbakia lortzen da, eta hau, 12. zenbaki lehena da.</li> <li><b>Nartzisista,</b> n digituko zenbakia da, haren digituak n. mailara berretzean eta batzean, zenbaki bera ematen dute. Adibidez, 153 = 1<sup>3</sup> + 5<sup>3</sup> + 3<sup>3</sup>.</li> <li><b>Omirp,</b> zenbaki lehen baten digituak trukatzean, beste zenbaki lehen bat ematen dute. Adibidez, 1597 eta 7951.</li> <li><b>Banpiro,</b> bere digituetatik lortutako bi zenbakiren biderkadurak, beste zenbaki lehen bat ematen du.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Beste_zenbaki_batzuk">Beste zenbaki batzuk</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=16" title="Aldatu atal hau: «Beste zenbaki batzuk»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=16" title="Edit section's source code: Beste zenbaki batzuk"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Erreal diren zenbakien artean, ekuazio aljebraikoen soluzio ez direnak <a href="/wiki/Zenbaki_transzendente" title="Zenbaki transzendente">transzendenteak</a> deritzegu; adibidez, <a href="/wiki/Pi_(zenbakia)" title="Pi (zenbakia)">Pi</a> eta <a href="/wiki/E_(zenbakia)" title="E (zenbakia)">e</a>. Bi zenbaki hauek <a href="/wiki/Eulerren_identitate" class="mw-redirect" title="Eulerren identitate">Eulerren identitatearen</a> bidez erlazionatuak daude. </p> <div class="mw-heading mw-heading3"><h3 id="Beste_zenbaki_batzuk_2">Beste zenbaki batzuk</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=17" title="Aldatu atal hau: «Beste zenbaki batzuk»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=17" title="Edit section's source code: Beste zenbaki batzuk"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Koaternioi" title="Koaternioi">Koaternioi</a></li> <li><a href="/wiki/Zenbaki_aljebraiko" title="Zenbaki aljebraiko">Zenbaki aljebraiko</a> <ul><li><a href="/wiki/Zenbaki_defektibo" title="Zenbaki defektibo">Zenbaki defektibo</a></li> <li><a href="/wiki/Zenbaki_kardinal" title="Zenbaki kardinal">Zenbaki kardinal</a></li> <li><a href="/wiki/Zenbaki_konposatu" title="Zenbaki konposatu">Zenbaki konposatu</a></li> <li><a href="/wiki/Zenbaki_lehen" title="Zenbaki lehen">Zenbaki lehen</a></li> <li><a href="/wiki/Zenbaki_oparo" title="Zenbaki oparo">Zenbaki oparo</a></li> <li><a href="/wiki/Zenbaki_ordinal" title="Zenbaki ordinal">Zenbaki ordinal</a></li> <li><a href="/wiki/Zenbaki_perfektu" title="Zenbaki perfektu">Zenbaki perfektu</a></li> <li><a href="/wiki/Zenbaki_alai" title="Zenbaki alai">Zenbaki alai</a></li> <li><a href="/wiki/Zero" title="Zero">Zero</a></li></ul></li> <li><a href="/wiki/Zenbaki_erreal" title="Zenbaki erreal">Zenbaki erreal</a></li> <li><a href="/w/index.php?title=Zenbaki_infinitu&action=edit&redlink=1" class="new" title="Zenbaki infinitu (sortu gabe)">Zenbaki infinitu</a></li> <li><a href="/wiki/Zenbaki_irrazional" title="Zenbaki irrazional">Zenbaki irrazional</a></li> <li><a href="/wiki/Zenbaki_konplexu" title="Zenbaki konplexu">Zenbaki konplexu</a></li></ul> <ul><li><ul><li><a href="/wiki/Zenbaki_bakoiti" title="Zenbaki bakoiti">Zenbaki bakoiti</a></li> <li><a href="/wiki/Zenbaki_bikoiti" title="Zenbaki bikoiti">Zenbaki bikoiti</a></li></ul></li> <li><a href="/wiki/Zenbaki-sistema" title="Zenbaki-sistema">Zenbaki-sistemak</a> <ul><li><a href="/wiki/Zenbaki-sistema_bitar" title="Zenbaki-sistema bitar">Zenbaki-sistema bitarra</a></li> <li><a href="/wiki/Zenbaki-sistema_hamartar" title="Zenbaki-sistema hamartar">Zenbaki-sistema hamartarra</a></li> <li><a href="/wiki/Zenbaki-sistema_hamaseitar" title="Zenbaki-sistema hamaseitar">Zenbaki-sistema hamaseitarra</a></li> <li><a href="/wiki/Zenbaki-sistema_zortzitar" title="Zenbaki-sistema zortzitar">Zenbaki-sistema zortzitarra</a></li></ul></li> <li><a href="/w/index.php?title=Zenbaki_transfinitu&action=edit&redlink=1" class="new" title="Zenbaki transfinitu (sortu gabe)">Zenbaki transfinitu</a></li> <li><a href="/wiki/Zenbaki_transzendente" title="Zenbaki transzendente">Zenbaki transzendente</a>: <a href="/wiki/Pi_(zenbakia)" title="Pi (zenbakia)">Π</a>, <a href="/wiki/E_(zenbakia)" title="E (zenbakia)">e</a></li></ul> <ul><li><a href="/wiki/Taxicab_zenbakia" title="Taxicab zenbakia">Taxicab zenbakiak</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Zenbakien_adierazpen_sistema">Zenbakien adierazpen sistema</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=18" title="Aldatu atal hau: «Zenbakien adierazpen sistema»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=18" title="Edit section's source code: Zenbakien adierazpen sistema"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Zifra,_digitu_eta_zenbakizko"><span id="Zifra.2C_digitu_eta_zenbakizko"></span>Zifra, digitu eta zenbakizko</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=19" title="Aldatu atal hau: «Zifra, digitu eta zenbakizko»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=19" title="Edit section's source code: Zifra, digitu eta zenbakizko"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbakiak letraz adierazteko modu ohikoenetako bat <i>sinboloen multzo finitu</i> bat edo digitu bat da, eta modu egokian konbinatuz, zenbaki gisa funtzionatzen duten zifrak eratzea ahalbidetzen du. Zeinu-sekuentzia jakin bat zenbaki bat irudikatzeko erabiltzen denean, zenbakizkoa deitzen zaio. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbakizko_oinarria">Zenbakizko oinarria</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=20" title="Aldatu atal hau: «Zenbakizko oinarria»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=20" title="Edit section's source code: Zenbakizko oinarria"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hizkuntza naturalek eta zifren bidez idazten diren zenbakiek arazoak izan ohi dituzte kopuru handiak adierazteko. Hori konpontzeko, matematika arloan oinarri aritmetiko bezala ezagutzen dena erabiltzen hasi zen, hau da, edozein zenbaki beste baten batuketaren edo biderketaren bidez adierazi zen. Adibidez, 13568 zenbaki arabiarra horrela banakatzen da: </p><p>8ak, azken zifra denez, <a href="/wiki/Unitate_(argipena)" class="mw-disambig" title="Unitate (argipena)">unitate</a>ak adierazten ditu; 6ak, <a href="/w/index.php?title=Hamarreko&action=edit&redlink=1" class="new" title="Hamarreko (sortu gabe)">hamarreko</a>ak; 5ak, <a href="/wiki/Ehuneko" title="Ehuneko">ehuneko</a>ak; 3ak, <a href="/w/index.php?title=Milakoa&action=edit&redlink=1" class="new" title="Milakoa (sortu gabe)">milako</a>ak; eta 1ak, hamar milakoak. Hau da: </p><p>1 · 10<sup>4</sup> + 3 · 10<sup>3</sup> + 4 · 10<sup>2</sup> + 6 · 10<sup>1</sup> + 8 · 10<sup>0</sup> = 13568 </p><p>Hizkuntza askok oinarri hamartarra erabiltzen dute, sistema arabiarrak bezala, beste hainbat hizkuntzatan, aldiz, ohikoa da hogei oinarriko sistemak erabiltzea. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbakiak_hizkuntza_naturaletan">Zenbakiak hizkuntza naturaletan</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=21" title="Aldatu atal hau: «Zenbakiak hizkuntza naturaletan»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=21" title="Edit section's source code: Zenbakiak hizkuntza naturaletan"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Hizkuntza_natural" title="Hizkuntza natural">Hizkuntza natural</a>ek izenak erabiltzen dituzte hatz bidezko zenbaketan oinarritutako zenbakietarako. Horregatik, hizkuntza gehienek 10 oinarriko (eskuetako hatzak) edo 20 oinarriko (esku eta oinetako hatzak) zenbaki-sistemak erabiltzen dituzte. </p> <div class="mw-heading mw-heading2"><h2 id="Ariketak"><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Fitxategi:Jakindun_logoa.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/24px-Jakindun_logoa.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/36px-Jakindun_logoa.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/48px-Jakindun_logoa.png 2x" data-file-width="225" data-file-height="225" /></a><figcaption></figcaption></figure> Ariketak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=22" title="Aldatu atal hau: «Ariketak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=22" title="Edit section's source code: Ariketak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-packed" style="background-color: #fef6e7; margin-left: 0;"> <li class="gallerycaption">Zenbakiak</li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Zenbaki_osoak_Ariketa_2_1_DBH.webm/320px--Zenbaki_osoak_Ariketa_2_1_DBH.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="214" height="120" data-durationhint="305" data-mwtitle="Zenbaki_osoak_Ariketa_2_1_DBH.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b1/Zenbaki_osoak_Ariketa_2_1_DBH.webm/Zenbaki_osoak_Ariketa_2_1_DBH.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b1/Zenbaki_osoak_Ariketa_2_1_DBH.webm/Zenbaki_osoak_Ariketa_2_1_DBH.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b1/Zenbaki_osoak_Ariketa_2_1_DBH.webm/Zenbaki_osoak_Ariketa_2_1_DBH.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/b/b1/Zenbaki_osoak_Ariketa_2_1_DBH.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b1/Zenbaki_osoak_Ariketa_2_1_DBH.webm/Zenbaki_osoak_Ariketa_2_1_DBH.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b1/Zenbaki_osoak_Ariketa_2_1_DBH.webm/Zenbaki_osoak_Ariketa_2_1_DBH.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/b/b1/Zenbaki_osoak_Ariketa_2_1_DBH.webm/Zenbaki_osoak_Ariketa_2_1_DBH.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span></span></div> <div class="gallerytext"><b>Zenbaki osoak</b> lantzeko ariketa.</div> </li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><span><video id="mwe_player_1" poster="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Zenbaki_osoak_Ariketa_1_DBH.webm/320px--Zenbaki_osoak_Ariketa_1_DBH.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="214" height="120" data-durationhint="316" data-mwtitle="Zenbaki_osoak_Ariketa_1_DBH.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/0b/Zenbaki_osoak_Ariketa_1_DBH.webm/Zenbaki_osoak_Ariketa_1_DBH.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/0b/Zenbaki_osoak_Ariketa_1_DBH.webm/Zenbaki_osoak_Ariketa_1_DBH.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/0b/Zenbaki_osoak_Ariketa_1_DBH.webm/Zenbaki_osoak_Ariketa_1_DBH.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/0/0b/Zenbaki_osoak_Ariketa_1_DBH.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/0b/Zenbaki_osoak_Ariketa_1_DBH.webm/Zenbaki_osoak_Ariketa_1_DBH.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/0b/Zenbaki_osoak_Ariketa_1_DBH.webm/Zenbaki_osoak_Ariketa_1_DBH.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/0b/Zenbaki_osoak_Ariketa_1_DBH.webm/Zenbaki_osoak_Ariketa_1_DBH.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span></span></div> <div class="gallerytext"><b>Zenbaki osoak</b> lantzeko ariketa II.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Erreferentziak">Erreferentziak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=23" title="Aldatu atal hau: «Erreferentziak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=23" title="Edit section's source code: Erreferentziak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation"><a rel="nofollow" class="external text" href="https://www.euskaltzaindia.eus/index.php?&option=com_hiztegianbilatu&task=bilaketa&Itemid=1693&lang=eu&nondik=0&zenbat=100&entryId=46532">«EH - Bilaketa - Bilaketa»</a> <i>www.euskaltzaindia.eus</i> <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-07-20)</small></span></span>.</span> </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation"><a rel="nofollow" class="external text" href="https://www.euskaltzaindia.eus/index.php?option=com_hiztegianbilatu&task=bilaketa&Itemid=1693&lang=eu&nondik=0&zenbat=100&non=osagaiakHasi&query=zifra&subcMota=&pos=&usgDomain=&usgGeo=&usgBeste=&usgReg=">«EH - Bilaketa - Bilaketa»</a> <i>www.euskaltzaindia.eus</i> <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-07-24)</small></span></span>.</span> </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> <span class="reference-text"><span class="citation"> <span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Ingelesez dago aipu honen iturburua"><b>(Ingelesez)</b></span></span> <span class="citation"><a rel="nofollow" class="external text" href="https://www.britannica.com/biography/Hippasus-of-Metapontum">«Hippasus of Metapontum | Greek philosopher | Britannica»</a> <i>www.britannica.com</i> <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-07-20)</small></span></span>.</span> </li> <li id="cite_note-4"><a href="#cite_ref-4">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFStewart,_Ian,_1945-">Stewart, Ian, 1945-.  (). <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/407170807"><i>Historia de las Matemáticas : en los ́ultimos 10.000 años. </i></a> Crítica, or. 13-14 or. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/978-84-7423-841-9" title="Berezi:BookSources/978-84-7423-841-9">978-84-7423-841-9</a>. <a href="/wiki/PubMed_Central" class="mw-redirect" title="PubMed Central">PMC</a> <a rel="nofollow" class="external text" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=407170807">407170807</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2020-11-13)</small></span></span>.</span> </li> <li id="cite_note-5"><a href="#cite_ref-5">↑</a> <span class="reference-text"><span class="citation"> <span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Ingelesez dago aipu honen iturburua"><b>(Ingelesez)</b></span></span> <span class="citation" id="CITEREFW.">W., Weisstein, Eric. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/NaturalNumber.html"><i>Natural Number. </i></a> <span class="reference-accessdate"><small>(Noiz kontsultatua: 2018-01-26)</small></span></span>.</span> </li> <li id="cite_note-6"><a href="#cite_ref-6">↑</a> <span class="reference-text"><span class="citation"> <span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Ingelesez dago aipu honen iturburua"><b>(Ingelesez)</b></span></span> <span class="citation"><a rel="nofollow" class="external text" href="https://www.chalkstreet.com/aptipedia/knowledgebase/base-system/">«Base system | ChalkStreet Aptipedia»</a> <i>ChalkStreet</i> <span class="reference-accessdate"><small>(Noiz kontsultatua: 2018-01-26)</small></span></span>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Ikus,_gainera"><span id="Ikus.2C_gainera"></span>Ikus, gainera</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=24" title="Aldatu atal hau: «Ikus, gainera»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=24" title="Edit section's source code: Ikus, gainera"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Matematika" title="Matematika">Matematika</a></li> <li><a href="/w/index.php?title=Oinarri_konstanteko_zenbaki-sistema&action=edit&redlink=1" class="new" title="Oinarri konstanteko zenbaki-sistema (sortu gabe)">Oinarri konstanteko zenbaki-sistema</a></li> <li><a href="/wiki/Zenbakizko_kognizioa" title="Zenbakizko kognizioa">Zenbakizko kognizioa</a></li> <li><a href="/wiki/Erromatar_zenbakera" title="Erromatar zenbakera">Erromatar zenbakera</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Kanpo_estekak">Kanpo estekak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbaki&veaction=edit&section=25" title="Aldatu atal hau: «Kanpo estekak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbaki&action=edit&section=25" title="Edit section's source code: Kanpo estekak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="clear:both;"></div><style data-mw-deduplicate="TemplateStyles:r7786466">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control,.mw-parser-output .mw-mf-linked-projects{border:1px solid #a2a9b1;font-size:88%}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}</style><div class="mw-authority-control"><div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r9236167">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px}.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}</style><style data-mw-deduplicate="TemplateStyles:r9236165">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px}.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}</style></div><div role="navigation" class="navbox" aria-labelledby="Autoritate_kontrola" style="width: inherit;padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Autoritate_kontrola" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Laguntza:Autoritate_kontrola" title="Laguntza:Autoritate kontrola">Autoritate kontrola</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><b>Wikimedia proiektuak</b></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datuak:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q11563" class="extiw" title="wikidata:Q11563">Q11563</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Numbers">Numbers</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q11563%22">Q11563</a></span></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikiesanak" title="Wikiquote"><img alt="Wikiquote" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/15px-Wikiquote-logo.svg.png" decoding="async" width="15" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/30px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span> Aipu famatuak:</span> <span class="uid"><a href="https://eu.wikiquote.org/wiki/Zenbaki" class="extiw" title="q:Zenbaki">Zenbaki</a></span></li></ul> <hr /> <ul><li><b>Identifikadoreak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioteca_Nacional_de_Espa%C3%B1a" class="mw-redirect" title="Biblioteca Nacional de España">BNE</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://datos.bne.es/resource/XX4678887">XX4678887</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioth%C3%A8que_nationale_de_France" class="mw-redirect" title="Bibliothèque nationale de France">BNF</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119326327">119326327</a> <a rel="nofollow" class="external text" href="http://data.bnf.fr/ark:/12148/cb119326327">(data)</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Integrated_Authority_File" class="mw-redirect" title="Integrated Authority File">GND</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4067271-2">4067271-2</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85093206">sh85093206</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/National_Diet_Library" class="mw-redirect" title="National Diet Library">NDL</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00571509">00571509</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/National_Library_of_the_Czech_Republic" class="mw-redirect" title="National Library of the Czech Republic">NKC</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph202644">ph202644</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Art_%26_Architecture_Thesaurus" title="Art & Architecture Thesaurus">AAT</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://vocab.getty.edu/page/aat/300055665">300055665</a></span></li> <li><b>Hiztegiak eta entziklopediak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Britannica</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/number-mathematics">url</a></span></li></ul> </div></td></tr></tbody></table></div><div class="mw-mf-linked-projects hlist"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datuak:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q11563" class="extiw" title="wikidata:Q11563">Q11563</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Numbers">Numbers</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q11563%22">Q11563</a></span></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikiesanak" title="Wikiquote"><img alt="Wikiquote" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/15px-Wikiquote-logo.svg.png" decoding="async" width="15" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/30px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span> Aipu famatuak:</span> <span class="uid"><a href="https://eu.wikiquote.org/wiki/Zenbaki" class="extiw" title="q:Zenbaki">Zenbaki</a></span></li></ul> </div></div>    </div><script>(RLQ=window.RLQ||[]).push(function(){mw.log.warn("Gadget \"ErrefAurrebista\" was not loaded. Please migrate it to use ResourceLoader. See \u003Chttps://eu.wikipedia.org/wiki/Berezi:Gadgetak\u003E.");});</script><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">"<a dir="ltr" href="https://eu.wikipedia.org/w/index.php?title=Zenbaki&oldid=9348011">https://eu.wikipedia.org/w/index.php?title=Zenbaki&oldid=9348011</a>"(e)tik eskuratuta</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Berezi:Kategoriak" title="Berezi:Kategoriak">Kategoriak</a>: <ul><li><a href="/wiki/Kategoria:Jakindunen_bideoak_dituzten_artikuluak" title="Kategoria:Jakindunen bideoak dituzten artikuluak">Jakindunen bideoak dituzten artikuluak</a></li><li><a href="/wiki/Kategoria:Zenbakiak" title="Kategoria:Zenbakiak">Zenbakiak</a></li><li><a href="/wiki/Kategoria:Objektu_matematikoak" title="Kategoria:Objektu matematikoak">Objektu matematikoak</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Ezkutuko kategoriak: <ul><li><a href="/wiki/Kategoria:Wikipedia_guztiek_izan_beharreko_artikuluak" title="Kategoria:Wikipedia guztiek izan beharreko artikuluak">Wikipedia guztiek izan beharreko artikuluak</a></li><li><a href="/wiki/Kategoria:Hezkuntza_Programako_artikuluak" title="Kategoria:Hezkuntza Programako artikuluak">Hezkuntza Programako artikuluak</a></li><li><a href="/wiki/Kategoria:Hezkuntza_Programa/Matematika" title="Kategoria:Hezkuntza Programa/Matematika">Hezkuntza Programa/Matematika</a></li><li><a href="/wiki/Kategoria:Wikipedia:BNE_identifikatzailea_duten_artikuluak" title="Kategoria:Wikipedia:BNE identifikatzailea duten artikuluak">Wikipedia:BNE identifikatzailea duten artikuluak</a></li><li><a href="/wiki/Kategoria:Wikipedia:BNF_identifikatzailea_duten_artikuluak" title="Kategoria:Wikipedia:BNF identifikatzailea duten artikuluak">Wikipedia:BNF identifikatzailea duten artikuluak</a></li><li><a href="/wiki/Kategoria:Wikipedia:GND_identifikatzailea_duten_artikuluak" title="Kategoria:Wikipedia:GND identifikatzailea duten artikuluak">Wikipedia:GND identifikatzailea duten artikuluak</a></li><li><a href="/wiki/Kategoria:Wikipedia:LCCN_identifikatzailea_duten_artikuluak" title="Kategoria:Wikipedia:LCCN identifikatzailea duten artikuluak">Wikipedia:LCCN identifikatzailea duten artikuluak</a></li><li><a href="/wiki/Kategoria:Wikipedia:AAT_identifikatzailea_duten_artikuluak" title="Kategoria:Wikipedia:AAT identifikatzailea duten artikuluak">Wikipedia:AAT identifikatzailea duten artikuluak</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"> Orriaren azken aldaketa: 29 uztaila 2023, 16:36.</li> <li id="footer-info-copyright">Testua <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.eu">Creative Commons Aitortu-PartekatuBerdin 4.0 lizentziari</a> jarraituz erabil daiteke; baliteke beste klausularen batzuk ere aplikatu behar izatea. Xehetasunen berri izateko, ikus <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">erabilera-baldintzak</a>.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Pribazitate politika</a></li> <li id="footer-places-about"><a href="/wiki/Laguntza:Wikipediari_buruz">Wikipediari buruz</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Erantzukizunen_mugaketa_orokorra">Lege oharra</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Garatzaileak</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/eu.wikipedia.org">Estatistikak</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie adierazpena</a></li> <li id="footer-places-mobileview"><a href="//eu.m.wikipedia.org/w/index.php?title=Zenbaki&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mugikorreko bista</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-55db797859-w5x4x","wgBackendResponseTime":164,"wgPageParseReport":{"limitreport":{"cputime":"0.461","walltime":"0.731","ppvisitednodes":{"value":4463,"limit":1000000},"postexpandincludesize":{"value":29654,"limit":2097152},"templateargumentsize":{"value":6774,"limit":2097152},"expansiondepth":{"value":17,"limit":100},"expensivefunctioncount":{"value":9,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":17014,"limit":5000000},"entityaccesscount":{"value":10,"limit":400},"timingprofile":["100.00% 446.573 1 -total"," 58.40% 260.792 1 Txantiloi:Autoritate_kontrola"," 13.15% 58.708 2 Txantiloi:Top_icon"," 12.12% 54.137 1 Txantiloi:Wikipedia1000"," 11.76% 52.498 1 Txantiloi:Erreferentzia_zerrenda"," 10.10% 45.107 2 Txantiloi:Category_handler"," 9.83% 43.891 6 Txantiloi:Erreferentzia"," 8.68% 38.766 12 Txantiloi:Erreferentzia/oinarria"," 7.06% 31.533 2 Txantiloi:Category_handler/numbered"," 6.44% 28.759 2 Txantiloi:Namespace_detect"]},"scribunto":{"limitreport-timeusage":{"value":"0.206","limit":"10.000"},"limitreport-memusage":{"value":3661620,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-6ffdb6f4f5-8tqms","timestamp":"20241205162007","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Zenbaki","url":"https:\/\/eu.wikipedia.org\/wiki\/Zenbaki","sameAs":"http:\/\/www.wikidata.org\/entity\/Q11563","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q11563","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-03-09T13:35:12Z","dateModified":"2023-07-29T15:36:13Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/7\/7e\/-bertsomate-_Zenbaki_motak.webm"}</script> </body> </html>