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-disabled skin-theme-clientpref-day vector-toc-available" lang="hu" dir="ltr"> <head> <meta charset="UTF-8"> <title>Injektív leképezés – Wikipédia</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-disabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )huwikimwclientpreferences=([^;]+)/);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":"ymd","wgMonthNames":["","január","február","március","április","május","június","július","augusztus","szeptember","október","november","december"],"wgRequestId":"20631283-f5c0-4410-986b-17669a8d6b0e","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Injektív_leképezés","wgTitle":"Injektív leképezés","wgCurRevisionId":26406985,"wgRevisionId":26406985,"wgArticleId":170161,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Analízis","Függvények","Halmazelmélet"],"wgPageViewLanguage":"hu","wgPageContentLanguage":"hu","wgPageContentModel":"wikitext","wgRelevantPageName":"Injektív_leképezés","wgRelevantArticleId":170161,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgRedirectedFrom":"Injektív_függvény","wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true, "wgFlaggedRevsParams":{"tags":{"accuracy":{"levels":2}}},"wgStableRevisionId":26406985,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"hu","pageLanguageDir":"ltr","pageVariantFallbacks":"hu"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":3000,"wgInternalRedirectTargetUrl":"/wiki/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s","wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q182003","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false, "wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.infobox":"ready","ext.gadget.wikiMenuStyles":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.flaggedRevs.basic":"ready","mediawiki.codex.messagebox.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["mediawiki.action.view.redirect","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.flaggedRevs.advanced","ext.gadget.wdsearch","ext.gadget.irclogin", "ext.gadget.ImageAnnotator.loader","ext.gadget.collapsible","ext.gadget.kepdia","ext.gadget.kinai","ext.gadget.poziciosTerkep","ext.gadget.wikiMenu","ext.gadget.wiwosm","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","oojs-ui.styles.icons-media","oojs-ui-core.icons","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=hu&modules=ext.flaggedRevs.basic%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cmediawiki.codex.messagebox.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=hu&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=hu&modules=ext.gadget.infobox%2CwikiMenuStyles&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=hu&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <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/0/02/Injection.svg/1200px-Injection.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1200"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Injection.svg/800px-Injection.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="800"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Injection.svg/640px-Injection.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="640"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Injektív leképezés – Wikipédia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//hu.m.wikipedia.org/wiki/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s"> <link rel="alternate" type="application/x-wiki" title="Szerkesztés" href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&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="Wikipédia (hu)"> <link rel="EditURI" type="application/rsd+xml" href="//hu.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://hu.wikipedia.org/wiki/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.hu"> <link rel="alternate" type="application/atom+xml" title="Wikipédia Atom-hírcsatorna" href="/w/index.php?title=Speci%C3%A1lis:Friss_v%C3%A1ltoztat%C3%A1sok&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-Injektív_leképezés rootpage-Injektív_leképezés skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Ugrás a tartalomhoz</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="Wiki"> <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="Főmenü" > <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">Főmenü</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">Főmenü</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">áthelyezés az oldalsávba</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">elrejtés</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigáció </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Kezd%C5%91lap" title="A kezdőlap megtekintése [z]" accesskey="z"><span>Kezdőlap</span></a></li><li id="n-sidebar-contents" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Tartalom"><span>Tartalom</span></a></li><li id="n-sidebar-featured" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Kiemelt_sz%C3%B3cikkek_list%C3%A1ja"><span>Kiemelt szócikkek</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Speci%C3%A1lis:Friss_v%C3%A1ltoztat%C3%A1sok" title="A wikiben történt legutóbbi változtatások listája [r]" accesskey="r"><span>Friss változtatások</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Speci%C3%A1lis:Lap_tal%C3%A1lomra" title="Egy véletlenszerűen kiválasztott lap betöltése [x]" accesskey="x"><span>Lap találomra</span></a></li><li id="n-sidebar-enquiries" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Tudakoz%C3%B3"><span>Tudakozó</span></a></li> </ul> </div> </div> <div id="p-sidebar-participate" class="vector-menu mw-portlet mw-portlet-sidebar-participate" > <div class="vector-menu-heading"> Részvétel </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-sidebar-basics" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:%C3%9Aj_szerkeszt%C5%91knek"><span>Kezdőknek</span></a></li><li id="n-sidebar-help" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Seg%C3%ADts%C3%A9g"><span>Segítség</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Port%C3%A1l:K%C3%B6z%C3%B6ss%C3%A9g" title="A projektről, miben segíthetsz, mit hol találsz meg"><span>Közösségi portál</span></a></li><li id="n-sidebar-contact" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Kapcsolatfelv%C3%A9tel"><span>Kapcsolatfelvétel</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Kezd%C5%91lap" 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="Wikipédia" src="/static/images/mobile/copyright/wikipedia-wordmark-fr.svg" style="width: 7.4375em; height: 1.125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-hu.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/Speci%C3%A1lis:Keres%C3%A9s" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Keresés a Wikipédián [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Keresés</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="Keresés a Wikipédián" aria-label="Keresés a Wikipédián" autocapitalize="sentences" title="Keresés a Wikipédián [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Speciális:Keresés"> </div> <button class="cdx-button cdx-search-input__end-button">Keresés</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Személyes eszközök"> <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="Megjelenés"> <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="Megjelenés" > <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">Megjelenés</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_hu.wikipedia.org&uselang=hu" class=""><span>Adományok</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=Speci%C3%A1lis:Szerkeszt%C5%91i_fi%C3%B3k_l%C3%A9trehoz%C3%A1sa&returnto=Injekt%C3%ADv+lek%C3%A9pez%C3%A9s" title="Arra bíztatunk, hogy hozz létre egy fiókot, és jelentkezz be, azonban ez nem kötelező" class=""><span>Fiók létrehozása</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=Speci%C3%A1lis:Bel%C3%A9p%C3%A9s&returnto=Injekt%C3%ADv+lek%C3%A9pez%C3%A9s" title="Bejelentkezni javasolt, de nem kötelező [o]" accesskey="o" class=""><span>Bejelentkezés</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="További lehetőségek" > <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="Személyes eszközök" > <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">Személyes eszközök</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Felhasználói menü" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_hu.wikipedia.org&uselang=hu"><span>Adományok</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:Szerkeszt%C5%91i_fi%C3%B3k_l%C3%A9trehoz%C3%A1sa&returnto=Injekt%C3%ADv+lek%C3%A9pez%C3%A9s" title="Arra bíztatunk, hogy hozz létre egy fiókot, és jelentkezz be, azonban ez nem kötelező"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Fiók létrehozása</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:Bel%C3%A9p%C3%A9s&returnto=Injekt%C3%ADv+lek%C3%A9pez%C3%A9s" title="Bejelentkezni javasolt, de nem kötelező [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Bejelentkezés</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"> Lapok kijelentkezett szerkesztőknek <a href="/wiki/Seg%C3%ADts%C3%A9g:Bevezet%C3%A9s" aria-label="Tudj meg többet a szerkesztésről"><span>további információk</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/Speci%C3%A1lis:K%C3%B6zrem%C5%B1k%C3%B6d%C3%A9seim" title="Erről az IP-címről végrehajtott szerkesztések listája [y]" accesskey="y"><span>Közreműködések</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speci%C3%A1lis:Vit%C3%A1m" title="Az általad használt IP-címről végrehajtott szerkesztések megvitatása [n]" accesskey="n"><span>Vitalap</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="Wiki"> <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="Tartalomjegyzék" 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">Tartalomjegyzék</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">áthelyezés az oldalsávba</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">elrejtés</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">Bevezető</div> </a> </li> <li id="toc-Definíció" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definíció"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definíció</span> </div> </a> <ul id="toc-Definíció-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Példák" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Példák"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Példák</span> </div> </a> <ul id="toc-Példák-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ellenpéldák" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ellenpéldák"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Ellenpéldák</span> </div> </a> <ul id="toc-Ellenpéldák-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Az_injekció_megfordítható" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Az_injekció_megfordítható"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Az injekció megfordítható</span> </div> </a> <ul id="toc-Az_injekció_megfordítható-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lásd_még" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lásd_még"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Lásd még</span> </div> </a> <ul id="toc-Lásd_még-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hivatkozások" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Hivatkozások"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Hivatkozások</span> </div> </a> <ul id="toc-Hivatkozások-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-További_információk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#További_információk"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>További információk</span> </div> </a> <ul id="toc-További_információk-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="Tartalomjegyzék" 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="Tartalomjegyzék kinyitása/becsukása" > <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">Tartalomjegyzék kinyitása/becsukása</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">Injektív leképezés</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="Ugrás egy más nyelvű szócikkre. Elérhető 55 nyelven" > <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-55" 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">55 nyelv</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Injective_function" title="Injective function – angol" lang="en" hreflang="en" data-title="Injective function" data-language-autonym="English" data-language-local-name="angol" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D9%84%D8%A9_%D9%85%D8%AA%D8%A8%D8%A7%D9%8A%D9%86%D8%A9" title="دالة متباينة – arab" lang="ar" hreflang="ar" data-title="دالة متباينة" data-language-autonym="العربية" data-language-local-name="arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%86%D0%BD%E2%80%99%D0%B5%D0%BA%D1%86%D1%8B%D1%8F_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Ін’екцыя (матэматыка) – belarusz" lang="be" hreflang="be" data-title="Ін’екцыя (матэматыка)" data-language-autonym="Беларуская" data-language-local-name="belarusz" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BD%D0%B5%D0%BA%D1%86%D0%B8%D1%8F" title="Инекция – bolgár" lang="bg" hreflang="bg" data-title="Инекция" data-language-autonym="Български" data-language-local-name="bolgár" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Injektivna_funkcija" title="Injektivna funkcija – bosnyák" lang="bs" hreflang="bs" data-title="Injektivna funkcija" data-language-autonym="Bosanski" data-language-local-name="bosnyák" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Funci%C3%B3_injectiva" title="Funció injectiva – katalán" lang="ca" hreflang="ca" data-title="Funció injectiva" data-language-autonym="Català" data-language-local-name="katalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%81%D8%A7%D9%86%DA%A9%D8%B4%D9%86%DB%8C_%DB%8C%DB%95%DA%A9%D8%A8%DB%95%DB%8C%DB%95%DA%A9" title="فانکشنی یەکبەیەک – közép-ázsiai kurd" lang="ckb" hreflang="ckb" data-title="فانکشنی یەکبەیەک" data-language-autonym="کوردی" data-language-local-name="közép-ázsiai kurd" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Prost%C3%A9_zobrazen%C3%AD" title="Prosté zobrazení – cseh" lang="cs" hreflang="cs" data-title="Prosté zobrazení" data-language-autonym="Čeština" data-language-local-name="cseh" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Injektiv" title="Injektiv – dán" lang="da" hreflang="da" data-title="Injektiv" data-language-autonym="Dansk" data-language-local-name="dán" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Injektive_Funktion" title="Injektive Funktion – német" lang="de" hreflang="de" data-title="Injektive Funktion" data-language-autonym="Deutsch" data-language-local-name="német" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%88%CE%BD%CE%B1_%CF%80%CF%81%CE%BF%CF%82_%CE%AD%CE%BD%CE%B1" title="Ένα προς ένα – görög" lang="el" hreflang="el" data-title="Ένα προς ένα" data-language-autonym="Ελληνικά" data-language-local-name="görög" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Dis%C4%B5eto" title="Disĵeto – eszperantó" lang="eo" hreflang="eo" data-title="Disĵeto" data-language-autonym="Esperanto" data-language-local-name="eszperantó" 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/Funci%C3%B3n_inyectiva" title="Función inyectiva – spanyol" lang="es" hreflang="es" data-title="Función inyectiva" data-language-autonym="Español" data-language-local-name="spanyol" 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/Injektiivne_funktsioon" title="Injektiivne funktsioon – észt" lang="et" hreflang="et" data-title="Injektiivne funktsioon" data-language-autonym="Eesti" data-language-local-name="észt" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Funtzio_injektibo" title="Funtzio injektibo – baszk" lang="eu" hreflang="eu" data-title="Funtzio injektibo" data-language-autonym="Euskara" data-language-local-name="baszk" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D8%A8%D8%B9_%DB%8C%DA%A9%E2%80%8C%D8%A8%D9%87%E2%80%8C%DB%8C%DA%A9" title="تابع یک‌به‌یک – perzsa" lang="fa" hreflang="fa" data-title="تابع یک‌به‌یک" data-language-autonym="فارسی" data-language-local-name="perzsa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Injektio" title="Injektio – finn" lang="fi" hreflang="fi" data-title="Injektio" data-language-autonym="Suomi" data-language-local-name="finn" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Injection_(math%C3%A9matiques)" title="Injection (mathématiques) – francia" lang="fr" hreflang="fr" data-title="Injection (mathématiques)" data-language-autonym="Français" data-language-local-name="francia" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Funci%C3%B3n_inxectiva" title="Función inxectiva – gallego" lang="gl" hreflang="gl" data-title="Función inxectiva" data-language-autonym="Galego" data-language-local-name="gallego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%97%D7%93-%D7%97%D7%93-%D7%A2%D7%A8%D7%9B%D7%99%D7%AA" title="פונקציה חד-חד-ערכית – héber" lang="he" hreflang="he" data-title="פונקציה חד-חד-ערכית" data-language-autonym="עברית" data-language-local-name="héber" 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%8F%E0%A4%95%E0%A5%88%E0%A4%95%E0%A5%80_%E0%A4%AB%E0%A4%B2%E0%A4%A8" title="एकैकी फलन – hindi" lang="hi" hreflang="hi" data-title="एकैकी फलन" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Injektivna_funkcija" title="Injektivna funkcija – horvát" lang="hr" hreflang="hr" data-title="Injektivna funkcija" data-language-autonym="Hrvatski" data-language-local-name="horvát" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Injection_(mathematica)" title="Injection (mathematica) – interlingva" lang="ia" hreflang="ia" data-title="Injection (mathematica)" data-language-autonym="Interlingua" data-language-local-name="interlingva" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fungsi_injektif" title="Fungsi injektif – indonéz" lang="id" hreflang="id" data-title="Fungsi injektif" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéz" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Funciono_injektiva" title="Funciono injektiva – idó" lang="io" hreflang="io" data-title="Funciono injektiva" data-language-autonym="Ido" data-language-local-name="idó" 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/Eint%C3%A6k_v%C3%B6rpun" title="Eintæk vörpun – izlandi" lang="is" hreflang="is" data-title="Eintæk vörpun" data-language-autonym="Íslenska" data-language-local-name="izlandi" 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/Funzione_iniettiva" title="Funzione iniettiva – olasz" lang="it" hreflang="it" data-title="Funzione iniettiva" data-language-autonym="Italiano" data-language-local-name="olasz" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8D%98%E5%B0%84" title="単射 – japán" lang="ja" hreflang="ja" data-title="単射" data-language-autonym="日本語" data-language-local-name="japán" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BD%D1%8A%D0%B5%D0%BA%D1%82%D0%B8%D0%B2%D1%82%D1%96_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Инъективті функция – kazah" lang="kk" hreflang="kk" data-title="Инъективті функция" data-language-autonym="Қазақша" data-language-local-name="kazah" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8B%A8%EC%82%AC_%ED%95%A8%EC%88%98" title="단사 함수 – koreai" lang="ko" hreflang="ko" data-title="단사 함수" data-language-autonym="한국어" data-language-local-name="koreai" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Functio_iniectiva" title="Functio iniectiva – latin" lang="la" hreflang="la" data-title="Functio iniectiva" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Fonzion_iniettiva" title="Fonzion iniettiva – lombard" lang="lmo" hreflang="lmo" data-title="Fonzion iniettiva" data-language-autonym="Lombard" data-language-local-name="lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Injekcija_(matematika)" title="Injekcija (matematika) – litván" lang="lt" hreflang="lt" data-title="Injekcija (matematika)" data-language-autonym="Lietuvių" data-language-local-name="litván" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%98%D0%BD%D1%98%D0%B5%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" title="Инјективна функција – macedón" lang="mk" hreflang="mk" data-title="Инјективна функција" data-language-autonym="Македонски" data-language-local-name="macedón" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Injectie_(wiskunde)" title="Injectie (wiskunde) – holland" lang="nl" hreflang="nl" data-title="Injectie (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="holland" 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/Injeksjon_i_matematikk" title="Injeksjon i matematikk – norvég (nynorsk)" lang="nn" hreflang="nn" data-title="Injeksjon i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norvég (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Injektiv_funksjon" title="Injektiv funksjon – norvég (bokmål)" lang="nb" hreflang="nb" data-title="Injektiv funksjon" data-language-autonym="Norsk bokmål" data-language-local-name="norvég (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Injeccion_(matematicas)" title="Injeccion (matematicas) – okszitán" lang="oc" hreflang="oc" data-title="Injeccion (matematicas)" data-language-autonym="Occitan" data-language-local-name="okszitán" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Funkcja_r%C3%B3%C5%BCnowarto%C5%9Bciowa" title="Funkcja różnowartościowa – lengyel" lang="pl" hreflang="pl" data-title="Funkcja różnowartościowa" data-language-autonym="Polski" data-language-local-name="lengyel" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fun%C3%A7%C3%A3o_injectiva" title="Função injectiva – portugál" lang="pt" hreflang="pt" data-title="Função injectiva" data-language-autonym="Português" data-language-local-name="portugál" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Func%C8%9Bie_injectiv%C4%83" title="Funcție injectivă – román" lang="ro" hreflang="ro" data-title="Funcție injectivă" data-language-autonym="Română" data-language-local-name="román" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D1%8A%D0%B5%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Инъекция (математика) – orosz" lang="ru" hreflang="ru" data-title="Инъекция (математика)" data-language-autonym="Русский" data-language-local-name="orosz" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Injective_function" title="Injective function – Simple English" lang="en-simple" hreflang="en-simple" data-title="Injective function" 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/Prost%C3%A9_zobrazenie" title="Prosté zobrazenie – szlovák" lang="sk" hreflang="sk" data-title="Prosté zobrazenie" data-language-autonym="Slovenčina" data-language-local-name="szlovák" 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/Injektivna_preslikava" title="Injektivna preslikava – szlovén" lang="sl" hreflang="sl" data-title="Injektivna preslikava" data-language-autonym="Slovenščina" data-language-local-name="szlovén" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%98%D0%BD%D1%98%D0%B5%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE_%D0%BF%D1%80%D0%B5%D1%81%D0%BB%D0%B8%D0%BA%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5" title="Инјективно пресликавање – szerb" lang="sr" hreflang="sr" data-title="Инјективно пресликавање" data-language-autonym="Српски / srpski" data-language-local-name="szerb" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Injektiv_funktion" title="Injektiv funktion – svéd" lang="sv" hreflang="sv" data-title="Injektiv funktion" data-language-autonym="Svenska" data-language-local-name="svéd" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Roztomajtowertno_funkcyjo" title="Roztomajtowertno funkcyjo – sziléziai" lang="szl" hreflang="szl" data-title="Roztomajtowertno funkcyjo" data-language-autonym="Ślůnski" data-language-local-name="sziléziai" 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%89%E0%AE%B3%E0%AF%8D%E0%AE%B3%E0%AE%BF%E0%AE%9F%E0%AF%81%E0%AE%95%E0%AF%8B%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81" title="உள்ளிடுகோப்பு – tamil" lang="ta" hreflang="ta" data-title="உள்ளிடுகோப்பு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9F%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B9%8C%E0%B8%8A%E0%B8%B1%E0%B8%99%E0%B8%AB%E0%B8%99%E0%B8%B6%E0%B9%88%E0%B8%87%E0%B8%95%E0%B9%88%E0%B8%AD%E0%B8%AB%E0%B8%99%E0%B8%B6%E0%B9%88%E0%B8%87" title="ฟังก์ชันหนึ่งต่อหนึ่ง – thai" lang="th" hreflang="th" data-title="ฟังก์ชันหนึ่งต่อหนึ่ง" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Birebir_fonksiyon" title="Birebir fonksiyon – török" lang="tr" hreflang="tr" data-title="Birebir fonksiyon" data-language-autonym="Türkçe" data-language-local-name="török" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%BD%27%D1%94%D0%BA%D1%86%D1%96%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Ін'єкція (математика) – ukrán" lang="uk" hreflang="uk" data-title="Ін'єкція (математика)" data-language-autonym="Українська" data-language-local-name="ukrán" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%C6%A1n_%C3%A1nh" title="Đơn ánh – vietnámi" lang="vi" hreflang="vi" data-title="Đơn ánh" data-language-autonym="Tiếng Việt" data-language-local-name="vietnámi" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8D%95%E5%B0%84" title="单射 – kínai" lang="zh" hreflang="zh" data-title="单射" data-language-autonym="中文" data-language-local-name="kínai" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%96%AE%E5%B0%84%E5%87%BD%E6%95%B8" title="單射函數 – kantoni" lang="yue" hreflang="yue" data-title="單射函數" data-language-autonym="粵語" data-language-local-name="kantoni" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q182003#sitelinks-wikipedia" title="Nyelvközi hivatkozások szerkesztése" class="wbc-editpage">Hivatkozások szerkesztése</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="Névterek"> <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/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s" title="A lap megtekintése [c]" accesskey="c"><span>Szócikk</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Vita:Injekt%C3%ADv_lek%C3%A9pez%C3%A9s" rel="discussion" title="Az oldal tartalmának megvitatása [t]" accesskey="t"><span>Vitalap</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="Nyelvvariáns váltása" > <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">magyar</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="Nézetek"> <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/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s"><span>Olvasás</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit" title="Az oldal forráskódjának szerkesztése [e]" accesskey="e"><span>Szerkesztés</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=history" title="A lap korábbi változatai [h]" accesskey="h"><span>Laptörténet</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Oldal eszközök"> <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="Eszközök" > <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">Eszközök</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">Eszközök</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">áthelyezés az oldalsávba</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">elrejtés</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="További lehetőségek" > <div class="vector-menu-heading"> Műveletek </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/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s"><span>Olvasás</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit" title="Az oldal forráskódjának szerkesztése [e]" accesskey="e"><span>Szerkesztés</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=history"><span>Laptörténet</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Általános </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speci%C3%A1lis:Mi_hivatkozik_erre/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s" title="Az erre a lapra hivatkozó más lapok listája [j]" accesskey="j"><span>Mi hivatkozik erre?</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speci%C3%A1lis:Kapcsol%C3%B3d%C3%B3_v%C3%A1ltoztat%C3%A1sok/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s" rel="nofollow" title="Az erről a lapról hivatkozott lapok utolsó változtatásai [k]" accesskey="k"><span>Kapcsolódó változtatások</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speci%C3%A1lis:Speci%C3%A1lis_lapok" title="Az összes speciális lap listája [q]" accesskey="q"><span>Speciális lapok</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&oldid=26406985" title="Állandó hivatkozás ezen lap ezen változatához"><span>Hivatkozás erre a változatra</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=info" title="További információk erről a lapról"><span>Lapinformációk</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:Hivatkoz%C3%A1s&page=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&id=26406985&wpFormIdentifier=titleform" title="Információk a lap idézésével kapcsolatban"><span>Hogyan hivatkozz erre a lapra?</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:UrlShortener&url=https%3A%2F%2Fhu.wikipedia.org%2Fwiki%2FInjekt%25C3%25ADv_lek%25C3%25A9pez%25C3%25A9s"><span>Rövidített URL készítése</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:QrCode&url=https%3A%2F%2Fhu.wikipedia.org%2Fwiki%2FInjekt%25C3%25ADv_lek%25C3%25A9pez%25C3%25A9s"><span>QR-kód letöltése</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"> Nyomtatás/exportálás </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=Speci%C3%A1lis:K%C3%B6nyv&bookcmd=book_creator&referer=Injekt%C3%ADv+lek%C3%A9pez%C3%A9s"><span>Könyv készítése</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:DownloadAsPdf&page=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=show-download-screen"><span>Letöltés PDF-ként</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&printable=yes" title="A lap nyomtatható változata [p]" accesskey="p"><span>Nyomtatható változat</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"> Társprojektek </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Injectivity" hreflang="en"><span>Wikimédia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q182003" title="Kapcsolt adattárelem [g]" accesskey="g"><span>Wikidata-adatlap</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="Oldal eszközök"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Megjelenés"> <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">Megjelenés</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">áthelyezés az oldalsávba</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">elrejtés</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-indicator-fr-review-status" class="mw-indicator"><indicator name="fr-review-status" class="mw-fr-review-status-indicator" id="mw-fr-revision-toggle"><span class="cdx-fr-css-icon-review--status--stable"></span><b>Ellenőrzött</b></indicator></div> </div> <div id="siteSub" class="noprint">A Wikipédiából, a szabad enciklopédiából</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(<a href="/w/index.php?title=Injekt%C3%ADv_f%C3%BCggv%C3%A9ny&redirect=no" class="mw-redirect" title="Injektív függvény">Injektív függvény</a> szócikkből átirányítva)</span><br /> <div id="mw-fr-revision-messages"><div id="mw-fr-revision-details" class="mw-fr-revision-details-dialog" style="display:none;"><div tabindex="0"></div><div class="cdx-dialog cdx-dialog--horizontal-actions"><header class="cdx-dialog__header cdx-dialog__header--default"><div class="cdx-dialog__header__title-group"><h2 class="cdx-dialog__header__title">Változat állapota</h2><p class="cdx-dialog__header__subtitle">Ez a lap egy ellenőrzött változata</p></div><button class="cdx-button cdx-button--action-default cdx-button--weight-quiet
							cdx-button--size-medium cdx-button--icon-only cdx-dialog__header__close-button" aria-label="Close" onclick="document.getElementById("mw-fr-revision-details").style.display = "none";" type="submit"><span class="cdx-icon cdx-icon--medium
							cdx-fr-css-icon--close"></span></button></header><div class="cdx-dialog__body">Ez a <a href="/wiki/Wikip%C3%A9dia:Jel%C3%B6lt_lapv%C3%A1ltozatok" title="Wikipédia:Jelölt lapváltozatok">közzétett változat</a>, <a class="external text" href="https://hu.wikipedia.org/w/index.php?title=Speci%C3%A1lis:Rendszernapl%C3%B3k&type=review&page=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s">ellenőrizve</a>: <i>2023. augusztus 31.</i><p><table id="mw-fr-revisionratings-box" class="flaggedrevs-color-1" style="margin: auto;" cellpadding="0"><tr><td class="fr-text" style="vertical-align: middle;">Pontosság</td><td class="fr-value40" style="vertical-align: middle;">ellenőrzött</td></tr></table></p></div></div><div tabindex="0"></div></div></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hu" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:Injection.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Injection.svg/200px-Injection.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Injection.svg/300px-Injection.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Injection.svg/400px-Injection.svg.png 2x" data-file-width="200" data-file-height="200" /></a><figcaption>Egy injektív függvény</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:Bijection.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Bijection.svg/200px-Bijection.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Bijection.svg/300px-Bijection.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Bijection.svg/400px-Bijection.svg.png 2x" data-file-width="200" data-file-height="200" /></a><figcaption>Egy másik injektív függvény, ami ráképezés is</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:Surjection.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Surjection.svg/200px-Surjection.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Surjection.svg/300px-Surjection.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Surjection.svg/400px-Surjection.svg.png 2x" data-file-width="200" data-file-height="200" /></a><figcaption>Egy <b>nem</b>-injektív függvény</figcaption></figure> <p>A <a href="/wiki/Matematika" title="Matematika">matematikában</a> <b>injekciónak</b>, <b>injektív leképezésnek</b>, <b>egy-egy értelmű leképezésnek</b> vagy <b>kölcsönösen egyértelmű leképezés</b>nek nevezzük azokat a <a href="/wiki/F%C3%BCggv%C3%A9ny_(matematika)" title="Függvény (matematika)">függvényeket</a>, melyek az értelmezési tartomány különböző elemeihez az értékkészlet különböző elemeit rendelik. (Nem tévesztendő össze a kölcsönösen egyértelmű <i>megfeleltetéssel</i>, mely a <a href="/wiki/Bijekci%C3%B3" title="Bijekció">bijektív függvény</a>.) </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definíció"><span id="Defin.C3.ADci.C3.B3"></span>Definíció</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit&section=1" title="Szakasz szerkesztése: Definíció"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Legyen <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"> <mi>A</mi> <mo>,</mo> <mi>B</mi> </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/96c3298ea9aa77c226be56a7d8515baaa517b90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.541ex; height:2.509ex;" alt="{\displaystyle A,B}"></span> tetszőleges halmazok és <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:A\to B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>A</mi> <mo stretchy="false">→</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:A\to B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20040a52d9391f2fe271f0aaa300bf7887a0c7b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.337ex; height:2.509ex;" alt="{\displaystyle f:A\to B}"></span> képező <a href="/wiki/Lek%C3%A9pez%C3%A9s" class="mw-redirect" title="Leképezés">leképezés</a>. Akkor mondjuk, hogy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> injekció, ha </p> <ul><li>tetszőleges <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\in A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>∈</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a,b\in A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/923af80638e57592b33fa715fb6c23651729fb73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.845ex; height:2.509ex;" alt="{\displaystyle a,b\in A}"></span> és <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(a)=f(b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(a)=f(b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f70209bf143b8417feef2aed98b2e86bc8f447e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.502ex; height:2.843ex;" alt="{\displaystyle f(a)=f(b)}"></span> esetén <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"> <mi>a</mi> <mo>=</mo> <mi>b</mi> </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/1956b03d1314c7071ac1f45ed7b1e29422dcfcc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.326ex; height:2.176ex;" alt="{\displaystyle a=b}"></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Példák"><span id="P.C3.A9ld.C3.A1k"></span>Példák</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit&section=2" title="Szakasz szerkesztése: Példák"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Az <a href="/wiki/Eg%C3%A9sz_sz%C3%A1mok" title="Egész számok">egész számok</a> halmazán értelmezett <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:\mathbf {Z} \to \mathbf {Z} ,a\mapsto 2a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mo>,</mo> <mi>a</mi> <mo stretchy="false">↦</mo> <mn>2</mn> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:\mathbf {Z} \to \mathbf {Z} ,a\mapsto 2a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d423013d788935ef8944b16a00c5ecef048c639f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.368ex; height:2.509ex;" alt="{\displaystyle f:\mathbf {Z} \to \mathbf {Z} ,a\mapsto 2a}"></span> függvény injekció.</li> <li>A <a href="/wiki/Term%C3%A9szetes_sz%C3%A1mok" title="Természetes számok">természetes számok</a> halmazán értelmezett <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:\mathbf {N} \to \mathbf {N} ,a\mapsto a+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo>,</mo> <mi>a</mi> <mo stretchy="false">↦</mo> <mi>a</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:\mathbf {N} \to \mathbf {N} ,a\mapsto a+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6158c501a15f57e4045ee0523cb2721b439ba518" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.123ex; height:2.509ex;" alt="{\displaystyle f:\mathbf {N} \to \mathbf {N} ,a\mapsto a+1}"></span> függvény injekció.</li> <li>Az <a href="/wiki/Eg%C3%A9sz_sz%C3%A1mok" title="Egész számok">egész számok</a> halmazán értelmezett <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:\mathbf {Z} \to \mathbf {Z} ,a\mapsto a+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mo>,</mo> <mi>a</mi> <mo stretchy="false">↦</mo> <mi>a</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:\mathbf {Z} \to \mathbf {Z} ,a\mapsto a+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9dc098d398f388ce1e8c53b29856f55ee7460c7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.208ex; height:2.509ex;" alt="{\displaystyle f:\mathbf {Z} \to \mathbf {Z} ,a\mapsto a+1}"></span> függvény injekció.</li> <li>Tetszőleges <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> halmazra az <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 id:X\to X,x\mapsto x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi>d</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mi>X</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">↦</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle id:X\to X,x\mapsto x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/733b0187d63977cd81d18e40bbd55350da6201dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.837ex; height:2.509ex;" alt="{\displaystyle id:X\to X,x\mapsto x}"></span> <a href="/wiki/F%C3%BCggv%C3%A9ny_(matematika)#Identitásfüggvény" title="Függvény (matematika)">identikus megfeleltetés</a> <b>injektív</b> leképezés.</li></ul> <p>(Az utolsó két példa, mivel nem csak injekció, hanem egyúttal <a href="/wiki/Sz%C3%BCrjekci%C3%B3" title="Szürjekció">szürjekció</a> is, ezért <a href="/wiki/Bijekci%C3%B3" title="Bijekció">bijekció</a>. Az első két példa nem <a href="/wiki/Sz%C3%BCrjekci%C3%B3" title="Szürjekció">szürjekció</a>.) </p> <div class="mw-heading mw-heading2"><h2 id="Ellenpéldák"><span id="Ellenp.C3.A9ld.C3.A1k"></span>Ellenpéldák</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit&section=3" title="Szakasz szerkesztése: Ellenpéldák"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>A <a href="/wiki/Val%C3%B3s_sz%C3%A1mok" title="Valós számok">valós számok</a> halmazán értelmezett <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 g:\mathbf {R} \to \mathbf {R} ,g(x)=x^{n}-x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mo>,</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g:\mathbf {R} \to \mathbf {R} ,g(x)=x^{n}-x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64bb5cb9b3de39623a4141de558556101c15f25f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.779ex; height:2.843ex;" alt="{\displaystyle g:\mathbf {R} \to \mathbf {R} ,g(x)=x^{n}-x}"></span> függvény nem injekció, ugyanis , például, <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 g(0)=g(1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(0)=g(1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/464fd70b41de388bb047041e204ca918469ac8de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.274ex; height:2.843ex;" alt="{\displaystyle g(0)=g(1)}"></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Az_injekció_megfordítható"><span id="Az_injekci.C3.B3_megford.C3.ADthat.C3.B3"></span>Az injekció megfordítható</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit&section=4" title="Szakasz szerkesztése: Az injekció megfordítható"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Egy másik definíció az injekcióra az, hogy olyan <a href="/wiki/Lek%C3%A9pez%C3%A9s" class="mw-redirect" title="Leképezés">leképezés</a>, melynek a megfeleltetésként (<a href="/wiki/Rel%C3%A1ci%C3%B3" title="Reláció">relációként</a>) vett <a href="/wiki/Rel%C3%A1ci%C3%B3_inverze" title="Reláció inverze">inverze</a> szintén függvény, bár az így kapott új függvény <a href="/wiki/%C3%89rtelmez%C3%A9si_tartom%C3%A1ny" class="mw-redirect" title="Értelmezési tartomány">értelmezési tartománya</a> az eredeti függvény <a href="/w/index.php?title=K%C3%A9phalmaz&action=edit&redlink=1" class="new" title="Képhalmaz (a lap nem létezik)">képhalmazának</a> csak egy <a href="/wiki/R%C3%A9szhalmaz" title="Részhalmaz">részhalmaza</a>. (Csak akkor egyezik meg vele, ha a kérdéses függvény egyúttal <a href="/wiki/Sz%C3%BCrjekci%C3%B3" title="Szürjekció">szürjekció</a>, és ezáltal így <a href="/wiki/Bijekci%C3%B3" title="Bijekció">bijekció</a> is). </p> <div class="mw-heading mw-heading2"><h2 id="Lásd_még"><span id="L.C3.A1sd_m.C3.A9g"></span>Lásd még</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit&section=5" title="Szakasz szerkesztése: Lásd még"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Sz%C3%BCrjekci%C3%B3" title="Szürjekció">Szürjekció</a></li> <li><a href="/wiki/Bijekci%C3%B3" title="Bijekció">Bijekció</a></li> <li><a href="/wiki/Izomorfizmus" class="mw-redirect" title="Izomorfizmus">Izomorfizmus</a></li> <li><a href="/w/index.php?title=Automorfizmus&action=edit&redlink=1" class="new" title="Automorfizmus (a lap nem létezik)">Automorfizmus</a></li> <li><a href="/wiki/Permut%C3%A1ci%C3%B3" title="Permutáció">Permutáció</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Hivatkozások"><span id="Hivatkoz.C3.A1sok"></span>Hivatkozások</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit&section=6" title="Szakasz szerkesztése: Hivatkozások"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Szendrei, Ágnes, <i>Diszkrét matematika</i>, Polygon, JATE Bolyai Intézet, Szeged (1994)</li></ul> <div class="mw-heading mw-heading2"><h2 id="További_információk"><span id="Tov.C3.A1bbi_inform.C3.A1ci.C3.B3k"></span>További információk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&action=edit&section=7" title="Szakasz szerkesztése: További információk"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://youproof.hu/kriptografia/13-adossag-ekvivalenciarelacio-ekvivalencia-osztaly-egesz-szam-homomorfizmus-beagyazas-negativ-szam">Alice és Bob - 13. rész: Alice és Bob eladósodik</a></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">A lap eredeti címe: „<a dir="ltr" href="https://hu.wikipedia.org/w/index.php?title=Injektív_leképezés&oldid=26406985">https://hu.wikipedia.org/w/index.php?title=Injektív_leképezés&oldid=26406985</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Wikip%C3%A9dia:Kateg%C3%B3ri%C3%A1k" title="Wikipédia:Kategóriák">Kategória</a>: <ul><li><a href="/wiki/Kateg%C3%B3ria:Anal%C3%ADzis" title="Kategória:Analízis">Analízis</a></li><li><a href="/wiki/Kateg%C3%B3ria:F%C3%BCggv%C3%A9nyek" title="Kategória:Függvények">Függvények</a></li><li><a href="/wiki/Kateg%C3%B3ria:Halmazelm%C3%A9let" title="Kategória:Halmazelmélet">Halmazelmélet</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"> A lap utolsó módosítása: 2023. augusztus 31., 21:11</li> <li id="footer-info-copyright">A lap szövege <a rel="nofollow" class="external text" href="http://creativecommons.org/licenses/by-sa/4.0/deed.hu">Creative Commons Nevezd meg! – Így add tovább! 4.0</a> licenc alatt van; egyes esetekben más módon is felhasználható. Részletekért lásd a <a href="/wiki/Wikip%C3%A9dia:Felhaszn%C3%A1l%C3%A1si_felt%C3%A9telek" title="Wikipédia:Felhasználási feltételek">felhasználási feltételeket</a>.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Adatvédelmi irányelvek</a></li> <li id="footer-places-about"><a href="/wiki/Wikip%C3%A9dia:R%C3%B3lunk">A Wikipédiáról</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikip%C3%A9dia:Jogi_nyilatkozat">Jogi nyilatkozat</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Magatartási kódex</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Fejlesztők</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/hu.wikipedia.org">Statisztikák</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Sütinyilatkozat</a></li> <li id="footer-places-mobileview"><a href="//hu.m.wikipedia.org/w/index.php?title=Injekt%C3%ADv_lek%C3%A9pez%C3%A9s&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobil nézet</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-6dfcdd5ff5-mkqbz","wgBackendResponseTime":263,"wgPageParseReport":{"limitreport":{"cputime":"0.035","walltime":"0.306","ppvisitednodes":{"value":113,"limit":1000000},"postexpandincludesize":{"value":0,"limit":2097152},"templateargumentsize":{"value":0,"limit":2097152},"expansiondepth":{"value":2,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":468,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 0.000 1 -total"]},"cachereport":{"origin":"mw-web.eqiad.main-67876799fc-2kxzl","timestamp":"20241127163415","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Injekt\u00edv lek\u00e9pez\u00e9s","url":"https:\/\/hu.wikipedia.org\/wiki\/Injekt%C3%ADv_lek%C3%A9pez%C3%A9s","sameAs":"http:\/\/www.wikidata.org\/entity\/Q182003","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q182003","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":"2007-05-07T13:10:39Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/0\/02\/Injection.svg","headline":"olyan lek\u00e9pez\u00e9s, ami k\u00fcl\u00f6nb\u00f6z\u0151 elemekhez k\u00fcl\u00f6nb\u00f6z\u0151 elemeket rendel"}</script> </body> </html>