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Hrvatskog Kraljevstva\"\u003E\u003Cimg src=\"//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/WPCRO_Logo_2014_f.svg/26px-WPCRO_Logo_2014_f.svg.png\" decoding=\"async\" width=\"26\" height=\"27\" class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/WPCRO_Logo_2014_f.svg/39px-WPCRO_Logo_2014_f.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/WPCRO_Logo_2014_f.svg/52px-WPCRO_Logo_2014_f.svg.png 2x\" data-file-width=\"150\" data-file-height=\"156\" /\u003E\u003C/a\u003E\u003C/span\u003E\u003C/td\u003E\u003Ctd class=\"mbox-text\"\u003EPišite i uređujte članke u \u003Cb\u003E\u003Ca href=\"/wiki/Wikipedija:Wikiprojekt_Hrvatska/1100._obljetnica_Hrvatskog_Kraljevstva\" title=\"Wikipedija:Wikiprojekt Hrvatska/1100. obljetnica Hrvatskog Kraljevstva\"\u003Ewikimaratonu povodom 1100. obljetnice Hrvatskoga Kraljevstva\u003C/a\u003E\u003C/b\u003E.\u003C/td\u003E\u003Ctd class=\"mbox-imageright\"\u003E\u003Cspan typeof=\"mw:File\"\u003E\u003Ca 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class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Treffpunkt.svg/60px-Treffpunkt.svg.png 2x\" data-file-width=\"512\" data-file-height=\"512\" /\u003E\u003C/span\u003E\u003C/span\u003E\u003C/td\u003E\u003Ctd class=\"mbox-text\"\u003EOtvoren je \u003Ca href=\"/wiki/Wikipedija:Zahtjev_za_komentare/Nazivi_%C4%8Dlanaka\" title=\"Wikipedija:Zahtjev za komentare/Nazivi članaka\"\u003E\u003Cb\u003EZahtjev za komentare o nazivima članaka\u003C/b\u003E\u003C/a\u003E\u003C/td\u003E\u003C/tr\u003E\u003C/tbody\u003E\u003C/table\u003E\n\u003Clink rel=\"mw-deduplicated-inline-style\" href=\"mw-data:TemplateStyles:r7100381\" /\u003E\u003Ctable class=\"plainlinks fmbox fmbox-system\" role=\"presentation\" style=\"border:2px solid #000000;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd class=\"mbox-image\"\u003E\u003Cspan typeof=\"mw:File\"\u003E\u003Ca href=\"/wiki/Wikipedija:Kafi%C4%87#Prijedlog_za_još_jednog_administratora_sučelja\" title=\"Wikipedija:Kafić\"\u003E\u003Cimg src=\"//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Ballot_icon.svg/40px-Ballot_icon.svg.png\" decoding=\"async\" width=\"26\" height=\"26\" class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Ballot_icon.svg/52px-Ballot_icon.svg.png 2x\" data-file-width=\"48\" data-file-height=\"48\" /\u003E\u003C/a\u003E\u003C/span\u003E\u003C/td\u003E\u003Ctd class=\"mbox-text\"\u003EU tijeku je \u003Ca href=\"/wiki/Wikipedija:Kafi%C4%87#Prijedlog_za_još_jednog_administratora_sučelja\" title=\"Wikipedija:Kafić\"\u003E\u003Cb\u003Eglasovanje za novog administratora sučelja\u003C/b\u003E\u003C/a\u003E (Ponor).\u003C/td\u003E\u003C/tr\u003E\u003C/tbody\u003E\u003C/table\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></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="Mrežno mjesto"> <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="Sadržaj" 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">Sadržaj</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</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">Početak</div> </a> </li> <li id="toc-Definicija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definicija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definicija</span> </div> </a> <ul id="toc-Definicija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Opisivanje_skupova" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Opisivanje_skupova"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Opisivanje skupova</span> </div> </a> <ul id="toc-Opisivanje_skupova-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Članstvo_skupa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Članstvo_skupa"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Članstvo skupa</span> </div> </a> <ul id="toc-Članstvo_skupa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kardinalnost_skupa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kardinalnost_skupa"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Kardinalnost skupa</span> </div> </a> <ul id="toc-Kardinalnost_skupa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Podskup" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Podskup"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Podskup</span> </div> </a> <ul id="toc-Podskup-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Posebni_skupovi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Posebni_skupovi"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Posebni skupovi</span> </div> </a> <ul id="toc-Posebni_skupovi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Unija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Unija"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Unija</span> </div> </a> <ul id="toc-Unija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Presjek" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Presjek"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Presjek</span> </div> </a> <ul id="toc-Presjek-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Komplementi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Komplementi"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Komplementi</span> </div> </a> <ul id="toc-Komplementi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-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="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Sadržaj" > <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="Prikaz sadržaja stranice" > <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">Prikaz sadržaja stranice</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">Skup</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="Idi na druge jezične varijante članka. Dostupan je na 103 jezika" > <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-103" 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">103 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Menge_(Mathematik)" title="Menge (Mathematik) – švicarski njemački" lang="gsw" hreflang="gsw" data-title="Menge (Mathematik)" data-language-autonym="Alemannisch" data-language-local-name="švicarski njemački" 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%88%B5%E1%89%A5%E1%88%B5%E1%89%A5" title="ስብስብ – amharski" lang="am" hreflang="am" data-title="ስብስብ" data-language-autonym="አማርኛ" data-language-local-name="amharski" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D8%A9_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="مجموعة (رياضيات) – arapski" lang="ar" hreflang="ar" data-title="مجموعة (رياضيات)" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Conxuntu" title="Conxuntu – asturijski" lang="ast" hreflang="ast" data-title="Conxuntu" data-language-autonym="Asturianu" data-language-local-name="asturijski" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C3%87oxluqlar" title="Çoxluqlar – azerbajdžanski" lang="az" hreflang="az" data-title="Çoxluqlar" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanski" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9A%D2%AF%D0%BC%D3%99%D0%BA%D0%BB%D0%B5%D0%BA" title="Күмәклек – baškirski" lang="ba" hreflang="ba" data-title="Күмәклек" data-language-autonym="Башҡортса" data-language-local-name="baškirski" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0" title="Мноства – bjeloruski" lang="be" hreflang="be" data-title="Мноства" data-language-autonym="Беларуская" data-language-local-name="bjeloruski" 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%9C%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0" title="Мноства – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Мноства" 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%9C%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Множество – bugarski" lang="bg" hreflang="bg" data-title="Множество" data-language-autonym="Български" data-language-local-name="bugarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%87%E0%A6%9F" title="সেট – bangla" lang="bn" hreflang="bn" data-title="সেট" data-language-autonym="বাংলা" data-language-local-name="bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Skup_(matematika)" title="Skup (matematika) – bosanski" lang="bs" hreflang="bs" data-title="Skup (matematika)" data-language-autonym="Bosanski" data-language-local-name="bosanski" 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/Conjunt" title="Conjunt – katalonski" lang="ca" hreflang="ca" data-title="Conjunt" data-language-autonym="Català" data-language-local-name="katalonski" 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/%DA%A9%DB%86%D9%85%DB%95%DA%B5%DB%95_(%D9%85%D8%A7%D8%AA%D9%85%D8%A7%D8%AA%DB%8C%DA%A9)" title="کۆمەڵە (ماتماتیک) – soranski kurdski" lang="ckb" hreflang="ckb" data-title="کۆمەڵە (ماتماتیک)" data-language-autonym="کوردی" data-language-local-name="soranski kurdski" 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/Mno%C5%BEina" title="Množina – češki" lang="cs" hreflang="cs" data-title="Množina" data-language-autonym="Čeština" data-language-local-name="češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%99%D1%8B%D1%88" title="Йыш – čuvaški" lang="cv" hreflang="cv" data-title="Йыш" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" 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/Set_(mathemateg)" title="Set (mathemateg) – velški" lang="cy" hreflang="cy" data-title="Set (mathemateg)" data-language-autonym="Cymraeg" data-language-local-name="velški" 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/M%C3%A6ngde" title="Mængde – danski" lang="da" hreflang="da" data-title="Mængde" data-language-autonym="Dansk" data-language-local-name="danski" 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/Menge_(Mathematik)" title="Menge (Mathematik) – njemački" lang="de" hreflang="de" data-title="Menge (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="njemački" 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%A3%CF%8D%CE%BD%CE%BF%CE%BB%CE%BF" title="Σύνολο – grčki" lang="el" hreflang="el" data-title="Σύνολο" data-language-autonym="Ελληνικά" data-language-local-name="grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Set_(mathematics)" title="Set (mathematics) – engleski" lang="en" hreflang="en" data-title="Set (mathematics)" data-language-autonym="English" data-language-local-name="engleski" 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/Aro_(matematiko)" title="Aro (matematiko) – esperanto" lang="eo" hreflang="eo" data-title="Aro (matematiko)" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Conjunto" title="Conjunto – španjolski" lang="es" hreflang="es" data-title="Conjunto" data-language-autonym="Español" data-language-local-name="španjolski" 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/Hulk" title="Hulk – estonski" lang="et" hreflang="et" data-title="Hulk" data-language-autonym="Eesti" data-language-local-name="estonski" 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/Multzo" title="Multzo – baskijski" lang="eu" hreflang="eu" data-title="Multzo" data-language-autonym="Euskara" data-language-local-name="baskijski" 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/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA)" title="مجموعه (ریاضیات) – perzijski" lang="fa" hreflang="fa" data-title="مجموعه (ریاضیات)" data-language-autonym="فارسی" data-language-local-name="perzijski" 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/Joukko" title="Joukko – finski" lang="fi" hreflang="fi" data-title="Joukko" data-language-autonym="Suomi" data-language-local-name="finski" 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/Hulk" title="Hulk – Võro" lang="vro" hreflang="vro" data-title="Hulk" 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/Seti" title="Seti – fidžijski" lang="fj" hreflang="fj" data-title="Seti" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fidžijski" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ensemble" title="Ensemble – francuski" lang="fr" hreflang="fr" data-title="Ensemble" data-language-autonym="Français" data-language-local-name="francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Insiemi" title="Insiemi – furlanski" lang="fur" hreflang="fur" data-title="Insiemi" data-language-autonym="Furlan" data-language-local-name="furlanski" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Tacar" title="Tacar – irski" lang="ga" hreflang="ga" data-title="Tacar" data-language-autonym="Gaeilge" data-language-local-name="irski" 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/%E9%9B%86%E5%90%88" title="集合 – gan kineski" lang="gan" hreflang="gan" data-title="集合" data-language-autonym="贛語" data-language-local-name="gan kineski" 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/Ansanm" title="Ansanm – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Ansanm" 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/Seata" title="Seata – škotski gaelski" lang="gd" hreflang="gd" data-title="Seata" data-language-autonym="Gàidhlig" data-language-local-name="škotski gaelski" 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/Conxunto" title="Conxunto – galicijski" lang="gl" hreflang="gl" data-title="Conxunto" data-language-autonym="Galego" data-language-local-name="galicijski" 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%A7%D7%91%D7%95%D7%A6%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="קבוצה (מתמטיקה) – hebrejski" lang="he" hreflang="he" data-title="קבוצה (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="hebrejski" 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%AE%E0%A5%81%E0%A4%9A%E0%A5%8D%E0%A4%9A%E0%A4%AF_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="समुच्चय (गणित) – hindski" lang="hi" hreflang="hi" data-title="समुच्चय (गणित)" data-language-autonym="हिन्दी" data-language-local-name="hindski" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Halmaz_(matematika)" title="Halmaz (matematika) – mađarski" lang="hu" hreflang="hu" data-title="Halmaz (matematika)" data-language-autonym="Magyar" data-language-local-name="mađarski" 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%B2%D5%A1%D5%A6%D5%B4%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Բազմություն – armenski" lang="hy" hreflang="hy" data-title="Բազմություն" data-language-autonym="Հայերեն" data-language-local-name="armenski" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Insimul" title="Insimul – interlingua" lang="ia" hreflang="ia" data-title="Insimul" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Himpunan_(matematika)" title="Himpunan (matematika) – indonezijski" lang="id" hreflang="id" data-title="Himpunan (matematika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" 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/Ensemblo" title="Ensemblo – ido" lang="io" hreflang="io" data-title="Ensemblo" data-language-autonym="Ido" data-language-local-name="ido" 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/Mengi" title="Mengi – islandski" lang="is" hreflang="is" data-title="Mengi" data-language-autonym="Íslenska" data-language-local-name="islandski" 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/Insieme" title="Insieme – talijanski" lang="it" hreflang="it" data-title="Insieme" data-language-autonym="Italiano" data-language-local-name="talijanski" 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/%E9%9B%86%E5%90%88" title="集合 – japanski" lang="ja" hreflang="ja" data-title="集合" data-language-autonym="日本語" data-language-local-name="japanski" 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/Set_(matimatix)" title="Set (matimatix) – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Set (matimatix)" 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-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%9B%E1%83%A0%E1%83%90%E1%83%95%E1%83%9A%E1%83%94" title="სიმრავლე – gruzijski" lang="ka" hreflang="ka" data-title="სიმრავლე" data-language-autonym="ქართული" data-language-local-name="gruzijski" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D3%A9%D0%BB%D1%96%D0%BA" title="Бөлік – kazaški" lang="kk" hreflang="kk" data-title="Бөлік" data-language-autonym="Қазақша" data-language-local-name="kazaški" 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%97%E0%B2%A3_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4)" title="ಗಣ (ಗಣಿತ) – karnatački" lang="kn" hreflang="kn" data-title="ಗಣ (ಗಣಿತ)" data-language-autonym="ಕನ್ನಡ" data-language-local-name="karnatački" 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%A7%91%ED%95%A9" title="집합 – korejski" lang="ko" hreflang="ko" data-title="집합" data-language-autonym="한국어" data-language-local-name="korejski" 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/Kom" title="Kom – kurdski" lang="ku" hreflang="ku" data-title="Kom" data-language-autonym="Kurdî" data-language-local-name="kurdski" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Copia" title="Copia – latinski" lang="la" hreflang="la" data-title="Copia" data-language-autonym="Latina" data-language-local-name="latinski" 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/Insemma" title="Insemma – lombardski" lang="lmo" hreflang="lmo" data-title="Insemma" data-language-autonym="Lombard" data-language-local-name="lombardski" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/El%C9%94ng%C9%94%CC%81t%C9%9B%CC%82_lisang%C3%A1" title="Elɔngɔ́tɛ̂ lisangá – lingala" lang="ln" hreflang="ln" data-title="Elɔngɔ́tɛ̂ lisangá" data-language-autonym="Lingála" data-language-local-name="lingala" class="interlanguage-link-target"><span>Lingála</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Aib%C4%97" title="Aibė – litavski" lang="lt" hreflang="lt" data-title="Aibė" data-language-autonym="Lietuvių" data-language-local-name="litavski" 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/Kopa" title="Kopa – latvijski" lang="lv" hreflang="lv" data-title="Kopa" data-language-autonym="Latviešu" data-language-local-name="latvijski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Множество – makedonski" lang="mk" hreflang="mk" data-title="Множество" data-language-autonym="Македонски" data-language-local-name="makedonski" 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%97%E0%B4%A3%E0%B4%82_(%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82)" title="ഗണം (ഗണിതം) – malajalamski" lang="ml" hreflang="ml" data-title="ഗണം (ഗണിതം)" data-language-autonym="മലയാളം" data-language-local-name="malajalamski" 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%9E%D0%BB%D0%BE%D0%BD%D0%BB%D0%BE%D0%B3" title="Олонлог – mongolski" lang="mn" hreflang="mn" data-title="Олонлог" data-language-autonym="Монгол" data-language-local-name="mongolski" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Set" title="Set – malajski" lang="ms" hreflang="ms" data-title="Set" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%85%E1%80%AF" title="အစု – burmanski" lang="my" hreflang="my" data-title="အစု" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmanski" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%92%D0%B5%D0%B9%D1%81%D1%81%D0%B0%D0%B5%D0%B2%D0%BA%D1%81" title="Вейссаевкс – mordvinski" lang="myv" hreflang="myv" data-title="Вейссаевкс" data-language-autonym="Эрзянь" data-language-local-name="mordvinski" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Koppel_(Mathematik)" title="Koppel (Mathematik) – donjonjemački" lang="nds" hreflang="nds" data-title="Koppel (Mathematik)" data-language-autonym="Plattdüütsch" data-language-local-name="donjonjemački" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Verzameling_(wiskunde)" title="Verzameling (wiskunde) – nizozemski" lang="nl" hreflang="nl" data-title="Verzameling (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="nizozemski" 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/Mengd" title="Mengd – norveški nynorsk" lang="nn" hreflang="nn" data-title="Mengd" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški 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/Mengde" title="Mengde – norveški bokmål" lang="nb" hreflang="nb" data-title="Mengde" data-language-autonym="Norsk bokmål" data-language-local-name="norveški bokmål" 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/Ensemble" title="Ensemble – Novial" lang="nov" hreflang="nov" data-title="Ensemble" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Ensemble" title="Ensemble – okcitanski" lang="oc" hreflang="oc" data-title="Ensemble" data-language-autonym="Occitan" data-language-local-name="okcitanski" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A9%88%E0%A9%B1%E0%A8%9F_(%E0%A8%97%E0%A8%A3%E0%A8%BF%E0%A8%A4)" title="ਸੈੱਟ (ਗਣਿਤ) – pandžapski" lang="pa" hreflang="pa" data-title="ਸੈੱਟ (ਗਣਿਤ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžapski" 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/Zbi%C3%B3r" title="Zbiór – poljski" lang="pl" hreflang="pl" data-title="Zbiór" data-language-autonym="Polski" data-language-local-name="poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Ansem" title="Ansem – Piedmontese" lang="pms" hreflang="pms" data-title="Ansem" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Conjunto" title="Conjunto – portugalski" lang="pt" hreflang="pt" data-title="Conjunto" data-language-autonym="Português" data-language-local-name="portugalski" 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/Tantachisqa" title="Tantachisqa – kečuanski" lang="qu" hreflang="qu" data-title="Tantachisqa" data-language-autonym="Runa Simi" data-language-local-name="kečuanski" 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/Mul%C8%9Bime" title="Mulțime – rumunjski" lang="ro" hreflang="ro" data-title="Mulțime" data-language-autonym="Română" data-language-local-name="rumunjski" 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%9C%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Множество – ruski" lang="ru" hreflang="ru" data-title="Множество" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Nzemi" title="Nzemi – sicilijski" lang="scn" hreflang="scn" data-title="Nzemi" data-language-autonym="Sicilianu" data-language-local-name="sicilijski" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Skup" title="Skup – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Skup" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpsko-hrvatski" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Set" title="Set – Simple English" lang="en-simple" hreflang="en-simple" data-title="Set" 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/Mno%C5%BEina" title="Množina – slovački" lang="sk" hreflang="sk" data-title="Množina" data-language-autonym="Slovenčina" data-language-local-name="slovački" 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/Mno%C5%BEica" title="Množica – slovenski" lang="sl" hreflang="sl" data-title="Množica" data-language-autonym="Slovenščina" data-language-local-name="slovenski" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Qaybta_(xisaab)" title="Qaybta (xisaab) – somalski" lang="so" hreflang="so" data-title="Qaybta (xisaab)" data-language-autonym="Soomaaliga" data-language-local-name="somalski" 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/Bashk%C3%ABsit%C3%AB" title="Bashkësitë – albanski" lang="sq" hreflang="sq" data-title="Bashkësitë" data-language-autonym="Shqip" data-language-local-name="albanski" 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%A1%D0%BA%D1%83%D0%BF" title="Скуп – srpski" lang="sr" hreflang="sr" data-title="Скуп" data-language-autonym="Српски / srpski" data-language-local-name="srpski" 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/M%C3%A4ngd" title="Mängd – švedski" lang="sv" hreflang="sv" data-title="Mängd" data-language-autonym="Svenska" data-language-local-name="švedski" 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/Mynga_(matymatyka)" title="Mynga (matymatyka) – šleski" lang="szl" hreflang="szl" data-title="Mynga (matymatyka)" data-language-autonym="Ślůnski" data-language-local-name="šleski" 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%95%E0%AE%A3%E0%AE%AE%E0%AF%8D_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="கணம் (கணிதம்) – tamilski" lang="ta" hreflang="ta" data-title="கணம் (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="tamilski" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B0%AE%E0%B0%BF%E0%B0%A4%E0%B1%81%E0%B0%B2%E0%B1%81" title="సమితులు – teluški" lang="te" hreflang="te" data-title="సమితులు" data-language-autonym="తెలుగు" data-language-local-name="teluški" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%8B%E0%B8%95_(%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="เซต (คณิตศาสตร์) – tajlandski" lang="th" hreflang="th" data-title="เซต (คณิตศาสตร์)" data-language-autonym="ไทย" data-language-local-name="tajlandski" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Pangkat_(matematika)" title="Pangkat (matematika) – tagalog" lang="tl" hreflang="tl" data-title="Pangkat (matematika)" data-language-autonym="Tagalog" data-language-local-name="tagalog" 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/K%C3%BCme" title="Küme – turski" lang="tr" hreflang="tr" data-title="Küme" data-language-autonym="Türkçe" data-language-local-name="turski" 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%9C%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD%D0%B0" title="Множина – ukrajinski" lang="uk" hreflang="uk" data-title="Множина" data-language-autonym="Українська" data-language-local-name="ukrajinski" 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%B7%D8%A7%D9%82%D9%85_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C)" title="طاقم (ریاضی) – urdski" lang="ur" hreflang="ur" data-title="طاقم (ریاضی)" data-language-autonym="اردو" data-language-local-name="urdski" 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/To%CA%BBplam_(matematika)" title="Toʻplam (matematika) – uzbečki" lang="uz" hreflang="uz" data-title="Toʻplam (matematika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%E1%BA%ADp_h%E1%BB%A3p_(to%C3%A1n_h%E1%BB%8Dc)" title="Tập hợp (toán học) – vijetnamski" lang="vi" hreflang="vi" data-title="Tập hợp (toán học)" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Verzoamelienge" title="Verzoamelienge – West Flemish" lang="vls" hreflang="vls" data-title="Verzoamelienge" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%9B%86%E5%90%88%EF%BC%88%E6%95%B0%E5%AD%A6%EF%BC%89" title="集合（数学） – wu kineski" lang="wuu" hreflang="wuu" data-title="集合（数学）" data-language-autonym="吴语" data-language-local-name="wu kineski" 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%9E%D0%BB%D0%BD" title="Олн – kalmyk" lang="xal" hreflang="xal" data-title="Олн" data-language-autonym="Хальмг" data-language-local-name="kalmyk" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%9B%E1%83%98%E1%83%90%E1%83%A0%E1%83%94" title="მიარე – Mingrelian" lang="xmf" hreflang="xmf" data-title="მიარე" 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%92%D7%A2%D7%96%D7%A2%D7%9E%D7%9C_(%D7%9E%D7%90%D7%98%D7%A2%D7%9E%D7%90%D7%98%D7%99%D7%A7)" title="געזעמל (מאטעמאטיק) – jidiš" lang="yi" hreflang="yi" data-title="געזעמל (מאטעמאטיק)" data-language-autonym="ייִדיש" data-language-local-name="jidiš" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%9B%86%E5%90%88_(%E6%95%B0%E5%AD%A6)" title="集合 (数学) – kineski" lang="zh" hreflang="zh" data-title="集合 (数学)" data-language-autonym="中文" data-language-local-name="kineski" 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/%E9%9B%86" title="集 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="集" 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/Chi%CC%8Dp-ha%CC%8Dp" title="Chi̍p-ha̍p – min nan kineski" lang="nan" hreflang="nan" data-title="Chi̍p-ha̍p" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan kineski" 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/%E9%9B%86%E5%90%88" title="集合 – kantonski" lang="yue" hreflang="yue" data-title="集合" data-language-autonym="粵語" data-language-local-name="kantonski" 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/Q36161#sitelinks-wikipedia" title="Poveznice na druge jezike" class="wbc-editpage">Uredi poveznice</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="Imenski prostori"> <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/Skup" title="Pogledaj sadržaj [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Razgovor:Skup" rel="discussion" title="Razgovorna stranica [t]" accesskey="t"><span>Razgovor</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="Promijeni jezičnu varijantu" > <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">hrvatski</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="Pogledi"> <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/Skup"><span>Čitaj</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Skup&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Skup&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Skup&action=history" title="Ranije izmjene na ovoj stranici [h]" accesskey="h"><span>Vidi povijest</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <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="Pomagala" > <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">Pomagala</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">Pomagala</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">sakrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Više mogućnosti" > <div class="vector-menu-heading"> Radnje </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/Skup"><span>Čitaj</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Skup&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Skup&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Skup&action=history"><span>Vidi povijest</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Razno </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:%C5%A0to_vodi_ovamo/Skup" title="Popis svih stranica koje sadrže poveznice na ovu stranicu [j]" accesskey="j"><span>Što vodi ovamo</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:Povezane_promjene/Skup" rel="nofollow" title="Nedavne promjene na stranicama koje su povezane s navedenom stranicom [k]" accesskey="k"><span>Povezane promjene</span></a></li><li id="t-upload" class="mw-list-item"><a href="//hr.wikipedia.org/wiki/Wikipedija:Upload" title="Postavi datoteke [u]" accesskey="u"><span>Postavi datoteku</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Skup&oldid=6434982" title="Trajna poveznica na ovu verziju stranice"><span>Trajna poveznica</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Skup&action=info" title="Više informacija o ovoj stranici"><span>Podatci o stranici</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Citiraj&page=Skup&id=6434982&wpFormIdentifier=titleform" title="Informacije o tome kako citirati ovu stranicu"><span>Citiraj ovu stranicu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:Skra%C4%87iva%C4%8D_adresa&url=https%3A%2F%2Fhr.wikipedia.org%2Fwiki%2FSkup"><span>Skraćeni URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrCode&url=https%3A%2F%2Fhr.wikipedia.org%2Fwiki%2FSkup"><span>Preuzmi QR kôd</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"> Ispis/izvoz </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=Posebno:Zbirka&bookcmd=book_creator&referer=Skup"><span>Stvori knjigu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Skup&action=show-download-screen"><span>Preuzmi kao PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Skup&printable=yes" title="Inačica za ispis ove stranice [p]" accesskey="p"><span>Inačica za ispis</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"> Wikimedijini projekti </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:Sets_(mathematics)" hreflang="en"><span>Zajednički poslužitelj</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/Q36161" title="Poveznica na stavku na projektu Wikipodatci [g]" accesskey="g"><span>Stavka na Wikipodatcima</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="Pomagala"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izgled"> <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">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Izvor: Wikipedija</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="hr" dir="ltr"><p>U <a href="/wiki/Matematika" title="Matematika">matematici</a>, <b>skup</b> se može shvatiti kao bilo koja kolekcija različitih apstraktnih objekata smatranim cjelinom. Iako se ovo čini jednostavnom idejom, skupovi su jedan od najvažnijih fundamentalnih koncepata u modernoj matematici.<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><sup class="reference" style="white-space:nowrap;">:21</sup> Matematička disciplina koja proučava moguće skupove, <a href="/wiki/Teorija_skupova" title="Teorija skupova">teorija skupova</a>, je sadržajno bogata i aktivna.<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><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><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><sup id="cite_ref-Allenby_5-0" class="reference"><a href="#cite_note-Allenby-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Teorija_skupova" title="Teorija skupova">Teorija skupova</a>, stvorena tek krajem 19. stoljeća, je danas sveprisutni dio matematičkog obrazovanja, te se stoga u većini zemalja uvodi već u osnovnoj školi. Teorija skupova se može shvatiti kao osnova nad kojom može biti izgrađena gotovo cijela matematika, te kao ishodište iz kojeg gotovo cijela matematika može biti izvedena. Ovaj članak predstavlja kratak i osnovni uvod u ono što matematičari zovu "intuitivna" ili "naivna" teorija - za više detalja pogledati <a href="/wiki/Naivna_teorija_skupova" title="Naivna teorija skupova">naivna teorija skupova</a>. Za rigorozniji i moderniji <a href="/wiki/Aksiom" title="Aksiom">aksiomatski</a> pristup skupovima, razvijena je aksiomatska teorija skupova. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Venn-diagram-AB.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/0/06/Venn-diagram-AB.svg/300px-Venn-diagram-AB.svg.png" decoding="async" width="300" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/0/06/Venn-diagram-AB.svg/450px-Venn-diagram-AB.svg.png 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/0/06/Venn-diagram-AB.svg/600px-Venn-diagram-AB.svg.png 2x" data-file-width="250" data-file-height="158" /></a><figcaption>Matematički odnos između skupova se može vizualizirati Vennovim dijagramom.</figcaption></figure> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definicija">Definicija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=1" title="Uredi odlomak: Definicija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=1" title="Uredi kôd odjeljka Definicija"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Na početku svog djela <i>Beiträge zur Begründung der transfiniten Mengenlehre</i>, <a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a>, principijelni tvorac teorije skupova, je napisao sljedeću definiciju skupa:<sup id="cite_ref-Allenby_5-1" class="reference"><a href="#cite_note-Allenby-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Pod terminom <i>skup</i> smatramo bilo koju kolekciju M određenih, različitih objekata m naše zamjedbe ili misli (koji će se zvati <i>elementi</i> skupa M) u cjelinu. </p><p>Objekte skupa također zovemo njegovim <i><a href="/wiki/%C4%8Clan_(matematika)" title="Član (matematika)">članovima</a></i> ili <i>elementima</i>. Elementi skupa mogu biti raznih vrsta: brojevi, ljudi, slova abecede, drugi skupovi itd. Skupovi se dogovorno označavaju velikim slovima <i>A</i>, <i>B</i>, <i>C</i>, itd. Za dva skupa <i>A</i> i <i>B</i> kažemo da su jednaka i zapisujemo <i>A</i> = <i>B</i> ako imaju iste članove. </p><p>Skup, za razliku od <a href="/w/index.php?title=Multiskup&action=edit&redlink=1" class="new" title="Multiskup (stranica ne postoji)">multiskupa</a>, ne može sadržavati više jednakih elemenata. Sve skupovne operacije čuvaju svojstvo jedinstvenosti elementa u skupu. Slično, redoslijed nabrajanja elemenata skupa je nebitan, za razliku od <i>slijeda</i> ili <i>tupla</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Opisivanje_skupova">Opisivanje skupova</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=2" title="Uredi odlomak: Opisivanje skupova" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=2" title="Uredi kôd odjeljka Opisivanje skupova"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nemaju svi skupovi precizan opis - neki mogu jednostavno biti proizvoljne kolekcije, bez nekog jasno izraženog "pravila" koje kazuje koji su elementi unutar ili van skupa. </p><p>Neki skupovi mogu biti opisani riječima, na primjer: </p> <dl><dd><i>A</i> je skup čiji su članovi prva četiri <a href="/wiki/Cijeli_broj" title="Cijeli broj">cijela broja</a>.</dd> <dd><i>B</i> je skup čiji su članovi boje hrvatske zastave.</dd></dl> <p>Dogovorno se skup također može definirati eksplicitnim nabrajanjem svih elemenata između vitičastih zagrada, na primjer: </p> <dl><dd><i>C</i> = {4, 2, 1, 3}</dd> <dd><i>D</i> = {crvena, bijela, plava}</dd></dl> <p>Dva različita opisa mogu definirati isti skup. Na primjer, gore definirani skupovi <i>A</i> i <i>C</i> su identični, pošto imaju jednake članove. Skraćeni zapis <i>A</i> = <i>C</i> se koristi za izražavanje takve jednakosti. Slično, za gore definirane skupove vrijedi <i>B</i> = <i>D</i>. </p><p>Identitet skupa ne ovisi o redoslijedu nabrajanja elemenata skupa, kao i o mogućim ponavljanjima elemenata prilikom nabrajanja. Na primjer, {6, 11} = {11, 6} = {11, 11, 6, 11}. </p><p>Za skupove s mnogo elemenata ponekad se koristi skraćena lista. Na primjer, prvih tisuću pozitivnih cijelih brojeva se mogu opisati simboličkom kraticom: </p> <dl><dd>{1, 2, 3, ..., 1000},</dd></dl> <p>pri čemu specijalni simbol od tri točke (<b>...</b>) označava da se lista nastavlja na podrazumijevani način. </p><p>Slično se skup <a href="/wiki/Parni_broj" class="mw-redirect" title="Parni broj">parnih brojeva</a> može opisati notacijom: </p> <dl><dd>{2, 4, 6, 8, ... }.</dd></dl> <p>Složeniji skupovi se ponekad opisuju različitom notacijom. Na primjer, skup <i>F</i> čiji su članovi prvih dvadeset brojeva koji su za četiri manji od kvadrata cijelog broja, može biti opisan na sljedeći način: </p> <dl><dd><i>F</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 n^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9810bbdafe4a6a8061338db0f74e25b7952620" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.676ex;" alt="{\displaystyle n^{2}}" /></span> – 4 <b>:</b> <i>n</i> je <a href="/wiki/Cijeli_broj" title="Cijeli broj">cijeli broj</a>; i 0 ≤ <i>n</i> ≤ 19}</dd></dl> <p>U ovom opisu, dvotočka (<b>:</b>) znači "takav da", i matematičari interpretiraju ovaj opis kao "<i>F</i> je skup svih brojeva oblika <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^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9810bbdafe4a6a8061338db0f74e25b7952620" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.676ex;" alt="{\displaystyle n^{2}}" /></span> – 4, takvih da je <i>n</i> cijeli broj u opsegu od 0 do 19 uključivo." (Ponekad se umjesto dvotočke koristi okomita crta <b>|</b>.) </p> <div class="mw-heading mw-heading2"><h2 id="Članstvo_skupa"><span id=".C4.8Clanstvo_skupa"></span>Članstvo skupa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=3" title="Uredi odlomak: Članstvo skupa" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=3" title="Uredi kôd odjeljka Članstvo skupa"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ako nešto jest ili nije element nekog pojedinačnog skupa, tada to simboliziramo sa <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 \in }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∈</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \in }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fe4d5b0a594c1da89b5e78e7dfbeed90bdcc32f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:1.843ex;" alt="{\displaystyle \in }" /></span> odnosno <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 \notin }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∉</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \notin }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33dea9a3a3f311cc734ffd570e8f697ea1560a90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.55ex; height:2.676ex;" alt="{\displaystyle \notin }" /></span>. Na primjer, u odnosu na već definirane skupove, vrijedi: </p> <dl><dd><ul><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 4\in A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mo>∈</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4\in A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/752a0e5b73d1b52e13aa59056b872cae13c109a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.746ex; height:2.176ex;" alt="{\displaystyle 4\in A}" /></span> 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 285\in F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>285</mn> <mo>∈</mo> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 285\in F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfd33bddf192ce1785910cecbb38c469c7294976" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.069ex; height:2.176ex;" alt="{\displaystyle 285\in F}" /></span> (budući da je 285 = 17² − 4); ali</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 9\notin F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>9</mn> <mo>∉</mo> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 9\notin F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8b612845c4aa73780b9bf4f410a74c1f541407" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.744ex; height:2.676ex;" alt="{\displaystyle 9\notin F}" /></span> 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 \mathrm {zelena} \ \notin B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">z</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> </mrow> <mtext> </mtext> <mo>∉</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {zelena} \ \notin B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d078f203f3b42bec8e2b21ef528537c9f516f5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.384ex; height:2.676ex;" alt="{\displaystyle \mathrm {zelena} \ \notin B}" /></span>.</li></ul></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Kardinalnost_skupa">Kardinalnost skupa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=4" title="Uredi odlomak: Kardinalnost skupa" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=4" title="Uredi kôd odjeljka Kardinalnost skupa"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Svaki gore opisan skup ima konačan broj članova - na primjer, skup <i>A</i> ima četiri člana, dok skup <i>B</i> ima tri člana. </p><p>Skup također može imati nula članova. Takav skup zove se <b><a href="/wiki/Prazni_skup" title="Prazni skup">prazni skup</a></b> i označava simbolom ø. Na primjer, skup <i>A</i> svih trostranih kvadrata ima nula članova, i stoga je <i>A</i> = ø. Poput broja nula, iako naizgled trivijalan, prazni se skup pokazao kao poprilično važan u matematici. </p><p>Skup također može imati beskonačan broj članova - na primjer, skup <a href="/wiki/Prirodni_broj" title="Prirodni broj">prirodnih brojeva</a> je beskonačan. </p><p>Kaže se da su dva skupa <b>ekvipotentna</b> (imaju <b>isti kardinalitet</b> ili su <b>jednakobrojni</b> ili su <b>bijektivni</b>) ako postoji <a href="/wiki/Funkcija#Klasifikacija_funkcija" class="mw-redirect mw-disambig" title="Funkcija">bijekcija</a> iz jednoga skupa u drugi skup. <a href="/wiki/Binarna_relacija" class="mw-redirect" title="Binarna relacija">Relacija</a> ekvipotencije je <a href="/wiki/Relacija_ekvivalencije" title="Relacija ekvivalencije">relacija ekvivalencije</a>, pa se skupovi svrstavaju u disjunktne klase - klasa kojoj pripada skup <i>S</i> zove se <b>kardinalni broj</b> skupa <i>S</i> i oznčava se sa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left|S\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>S</mi> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|S\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70d6f6587b1ee1ed475033557c25f9534e02fa4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.793ex; height:2.843ex;" alt="{\displaystyle \left|S\right|}" /></span> ili card <i>S</i> ili <i>#S</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Podskup">Podskup</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=5" title="Uredi odlomak: Podskup" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=5" title="Uredi kôd odjeljka Podskup"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><style data-mw-deduplicate="TemplateStyles:r7016135">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Podskup" title="Podskup">Podskup</a></div></i></div> <p>Ako je svaki član skupa <i>A</i> također član skupa <i>B</i>, tada se za <i>A</i> kaže da je <b>podskup</b> od <i>B</i>, piše se <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\subseteq 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\subseteq B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b09068bd2f7ba899aeb883ebe670b2ad07b0c851" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.606ex; height:2.343ex;" alt="{\displaystyle A\subseteq B}" /></span>, te izgovara <i>A je sadržan u B</i>. Može se, također, zapisati <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\supseteq A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>⊇</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B\supseteq A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2fd7d8e0fa00d29c0d6a35ab2c3d4cd636bd136" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.606ex; height:2.343ex;" alt="{\displaystyle B\supseteq A}" /></span> što se čita kao <i>B je nadskup od A</i>, <i>B uključuje A</i> ili <i>B sadrži A</i>. Relacija između skupova uspostavljenu sa <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 \subseteq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊆</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \subseteq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a924f8dcb2847bb8871edfdbf4c6b5cca0669228" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \subseteq }" /></span> zove se <b>inkluzija</b>. </p><p>Ako je <i>A</i> podskup i nije jednak skupu <i>B</i>, tada se za <i>A</i> kaže da je <b>pravi podskup</b> skupa <i>B</i>, zapisuje s <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\subset 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\subset B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/010e98bb4c817357e3ef7e8fa7fbe2385b2aec6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.606ex; height:2.176ex;" alt="{\displaystyle A\subset B}" /></span> (<i>A je pravi podskup od B</i>) ili <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\supset A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>⊃</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B\supset A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/450398271587fcd521f7313ee3ebfdb5023e1c07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.606ex; height:2.176ex;" alt="{\displaystyle B\supset A}" /></span> (<i>B je pravi nadskup od A</i>). Međutim, u nekoj literaturi ovi se simboli čitaju isto kao 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 \subseteq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊆</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \subseteq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a924f8dcb2847bb8871edfdbf4c6b5cca0669228" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \subseteq }" /></span> 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 \supseteq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊇</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \supseteq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c8a31abf11074afa03a75eba80bfce6b98020e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \supseteq }" /></span>, te se stoga češto preferira korištenje eksplicitnijih simbola <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 \subsetneq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊊</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \subsetneq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ccda11a9c5eb10088602771f7c0f05ffea7f41c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.509ex;" alt="{\displaystyle \subsetneq }" /></span> 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 \supsetneq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊋</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \supsetneq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b84cda99291cdfefb94e6f580e14da12d3f43009" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.509ex;" alt="{\displaystyle \supsetneq }" /></span> za prave podskupove i nadskupove. </p> <div style="float:right;margin:1em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/Datoteka:Venn_A_subset_B.png" class="mw-file-description" title="A je podskup od B"><img alt="A je podskup od B" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Venn_A_subset_B.png/250px-Venn_A_subset_B.png" decoding="async" width="150" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/d/d6/Venn_A_subset_B.png 2x" data-file-width="294" data-file-height="210" /></a><figcaption>A je podskup od B</figcaption></figure><center><small> <i>A</i> je podskup od <i>B</i></small></center></div> <p>Primjeri: </p> <dl><dd><ul><li>Skup svih žena je pravi podskup skupa svih ljudi.</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 \{1,3\}\subset \{1,2,3,4\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo fence="false" stretchy="false">}</mo> <mo>⊂</mo> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{1,3\}\subset \{1,2,3,4\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53f939503daa20a005d11af108adfc07893c2b46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.859ex; height:2.843ex;" alt="{\displaystyle \{1,3\}\subset \{1,2,3,4\}}" /></span></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 \{1,2,3,4\}\subseteq \{1,2,3,4\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo fence="false" stretchy="false">}</mo> <mo>⊆</mo> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{1,2,3,4\}\subseteq \{1,2,3,4\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9805912e7dbfff7bb063a88e9eb27c700550d256" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.252ex; height:2.843ex;" alt="{\displaystyle \{1,2,3,4\}\subseteq \{1,2,3,4\}}" /></span></li></ul></dd></dl> <p>Prazni skup je podskup svakog skupa i svaki skup je sam svoj podskup: </p> <dl><dd><ul><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 \emptyset \subseteq A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∅</mi> <mo>⊆</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \emptyset \subseteq A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/101ea28c34ece6f8f6a828d5326e25cd334fc084" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.004ex; height:2.509ex;" alt="{\displaystyle \emptyset \subseteq A}" /></span></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 A\subseteq A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>⊆</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\subseteq A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1ce5093be9e30238b83393aed738eafd3a43030" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.585ex; height:2.343ex;" alt="{\displaystyle A\subseteq A}" /></span></li></ul></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Posebni_skupovi">Posebni skupovi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=6" title="Uredi odlomak: Posebni skupovi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=6" title="Uredi kôd odjeljka Posebni skupovi"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Neki istaknuti skupovi imaju izuzetnu matematičku važnosti i toliko se često koriste da su dobili posebna imena i notaciju. Jedan od njih je već spomenuti prazni skup. Neki od ostalih su: </p> <ul><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 \mathbb {P} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">P</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {P} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1053af9e662ceaf56c4455f90e0f67273422eded" 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 \mathbb {P} }" /></span> označava skup svih <a href="/wiki/Prost_broj" class="mw-redirect" title="Prost broj">prostih brojeva</a>.</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 \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> označava skup svih <a href="/wiki/Prirodni_broj" title="Prirodni broj">prirodnih brojeva</a>. Drugim riječima, <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> = {1, 2, 3, ...}, ili rjeđe <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> = {0, 1, 2, 3, ...}.</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 \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> označava skup svih <a href="/wiki/Cijeli_broj" title="Cijeli broj">cijelih brojeva</a> (bilo pozitivnih, negativnih ili nule). Stoga je <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> = {..., -2, -1, 0, 1, 2, ...}.</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 \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> označava skup svih <a href="/wiki/Racionalni_broj" title="Racionalni broj">racionalnih brojeva</a> (tj. skup svih pravih i nepravih razlomaka). Stoga je <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> = {<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 {\begin{matrix}{\frac {a}{b}}\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}{\frac {a}{b}}\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5fa8dd7ee3b49dceb1cf498088d34d2ba943e00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.457ex; height:3.509ex;" alt="{\displaystyle {\begin{matrix}{\frac {a}{b}}\end{matrix}}}" /></span> : <i>a</i>,<i>b</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 \in \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \in \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf4280f3eac3f807374942067347c9219670bb81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.746ex; height:2.176ex;" alt="{\displaystyle \in \mathbb {Z} }" /></span> i <i>b</i> ≠ 0}. Na primjer, <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 {\begin{matrix}{\frac {1}{4}}\end{matrix}}\in \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}{\frac {1}{4}}\end{matrix}}\in \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38ca42663a21b12e00a899a1cb53027d1f13810b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.977ex; margin-bottom: -0.194ex; width:7.058ex; height:3.509ex;" alt="{\displaystyle {\begin{matrix}{\frac {1}{4}}\end{matrix}}\in \mathbb {Q} }" /></span> 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 {\begin{matrix}{\frac {11}{6}}\end{matrix}}\in \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>11</mn> <mn>6</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}{\frac {11}{6}}\end{matrix}}\in \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2de037bdd7a4858a4c65dd523a1b52e07027a95a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:7.88ex; height:3.509ex;" alt="{\displaystyle {\begin{matrix}{\frac {11}{6}}\end{matrix}}\in \mathbb {Q} }" /></span>. Svi cijeli brojevi su u ovom skupu jer se svaki cijeli broj <i>a</i> može izraziti kao razlomak <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 {\begin{matrix}{\frac {a}{1}}\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mn>1</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}{\frac {a}{1}}\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/126f7861b55876f26f549db85024c7d16ae914c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.833ex; margin-bottom: -0.172ex; width:2.457ex; height:3.176ex;" alt="{\displaystyle {\begin{matrix}{\frac {a}{1}}\end{matrix}}}" /></span>.</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 \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> je skup svih <a href="/wiki/Realni_broj" title="Realni broj">realnih brojeva</a>. Ovaj skup uključuje sve racionalne i iracionalne brojeve (tj. brojeve koji se ne mogu zapisati u obliku razlomka, kao što su <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> <mo>,</mo> </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/47495546dd4b7607bbcb5658efe66abaf1955034" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.979ex; height:2.009ex;" alt="{\displaystyle \pi ,}" /></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 e,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cfc3e7aeae6ef256412eaa9f68d097804943b5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.73ex; height:2.009ex;" alt="{\displaystyle e,}" /></span> i √2).</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 \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> je skup svih <a href="/wiki/Kompleksni_broj" title="Kompleksni broj">kompleksnih brojeva</a>.</li></ul> <p>Svaki od ovih skupova brojeva je <a href="/wiki/Beskona%C4%8Dan_skup" title="Beskonačan skup">beskonačan</a>, premda vrijedi <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 {P} \subset \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">P</mi> </mrow> <mo>⊂</mo> <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 {P} \subset \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/9c68bcc859fda88697835267c757b2199d9a5d4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.305ex; height:2.509ex;" alt="{\displaystyle \mathbb {P} \subset \mathbb {N} \subset \mathbb {Z} \subset \mathbb {Q} \subset \mathbb {R} \subset \mathbb {C} }" /></span>, iako se prosti brojevi općenito koriste manje od ostalih skupova izvan <a href="/wiki/Teorija_brojeva" title="Teorija brojeva">teorije brojeva</a> i srodnih disciplina. </p><p>Međutim, ne postoji samo jedna vrsta beskonačnosti. Za skup koji je ekvipotentan (jednakobrojan) sa skupom prirodnih brojeva <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> kažemo da je <b>prebrojivo beskonačan</b> (kraće <i>prebrojiv</i>), a "veći" skupovi su <b>neprebrojivo beskonačni</b> (kraće <i>neprebrojivi</i>). </p><p>Prebrojivo beskonačni skupovi su, na primjer, skupovi <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 {P} ,\mathbb {N} ,\mathbb {Z} ,\mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">P</mi> </mrow> <mo>,</mo> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {P} ,\mathbb {N} ,\mathbb {Z} ,\mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33188fa1ead7cb1859f62f5ef3552fddf97af0c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.559ex; height:2.509ex;" alt="{\displaystyle \mathbb {P} ,\mathbb {N} ,\mathbb {Z} ,\mathbb {Q} }" /></span>, kao i skup svih prirodnih brojeva koji su parni, neparni, djeljivi s 3, djeljivi 4, itd. Primjeri neprebrojivo beskonačnih skupova su <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> 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 \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>. </p> <div class="mw-heading mw-heading2"><h2 id="Unija">Unija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=7" title="Uredi odlomak: Unija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=7" title="Uredi kôd odjeljka Unija"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135" /><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Unija_skupova" title="Unija skupova">Unija skupova</a></div></i></div> <p>Postoji nekoliko načina za konstruiranje novih skupova od već postojećih. Dva se skupa mogu "zbrojiti". <b>Unija</b> skupova <i>A</i> i <i>B</i>, označena s <i>A</i> U <i>B</i>, je skup svih elemenata koji su članovi ili skupa <i>A</i> ili skupa <i>B</i>. </p> <div style="float:right;margin:1em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/Datoteka:Venn_A_union_B.png" class="mw-file-description" title="A unija B"><img alt="A unija B" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Venn_A_union_B.png/150px-Venn_A_union_B.png" decoding="async" width="150" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Venn_A_union_B.png/225px-Venn_A_union_B.png 1.5x, //upload.wikimedia.org/wikipedia/commons/2/2f/Venn_A_union_B.png 2x" data-file-width="271" data-file-height="186" /></a><figcaption>A unija B</figcaption></figure><center><small> <b>Unija</b> skupova <i>A</i> i <i>B</i></small></center></div> <p>Primjeri: </p> <dl><dd><ul><li>{1, 2} U {crvena, bijela} = {1, 2, crvena, bijela}</li> <li>{1, 2, zelena} U {crvena, bijela, zelena} = {1, 2, crvena, bijela, zelena}</li> <li>{1, 2} U {1, 2} = {1, 2}</li></ul></dd></dl> <p>Neka osnovna svojstva unije: </p> <dl><dd><ul><li><i>A</i> U <i>B</i>   =   <i>B</i> U <i>A</i></li> <li><i>A</i>  je podskup skupa  <i>A</i> U <i>B</i></li> <li><i>A</i> U <i>A</i>   =  <i>A</i></li> <li><i>A</i> U ø   =  <i>A</i></li></ul></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Presjek">Presjek</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=8" title="Uredi odlomak: Presjek" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=8" title="Uredi kôd odjeljka Presjek"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135" /><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Presjek_skupova" title="Presjek skupova">Presjek skupova</a></div></i></div> <p>Novi se skup također može konstruirati određivanjem "zajedničkih" elemenata obaju skupova. <b>Presjek</b> skupova <i>A</i> i <i>B</i>, označen s <i>A</i> ∩ <i>B</i>, je skup svih elemenata koji su članovi i skupa <i>A</i> i skupa <i>B</i>. Ako je <i>A</i> ∩ <i>B</i>  =  ø, tada za <i>A</i> i <i>B</i> kažemo da su <b>disjunktni</b>. </p> <div style="float:right;margin:1em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/Datoteka:Venn_A_intersect_B.svg" class="mw-file-description" title="A presjek B"><img alt="A presjek B" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/250px-Venn_A_intersect_B.svg.png" decoding="async" width="150" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/330px-Venn_A_intersect_B.svg.png 2x" data-file-width="350" data-file-height="250" /></a><figcaption>A presjek B</figcaption></figure><center><small><b>Presjek</b> skupova <i>A</i> i <i>B</i></small></center></div> <p>Primjer: </p> <dl><dd><ul><li>{1, 2} ∩ {crvena, bijela} = ø</li> <li>{1, 2, zelena} ∩ {crvena, bijela, zelena} = {zelena}</li> <li>{1, 2} ∩ {1, 2} = {1, 2}</li></ul></dd></dl> <p>Neka osnovna svojstva presjeka: </p> <dl><dd><ul><li><i>A</i> ∩ <i>B</i>   =   <i>B</i> ∩ <i>A</i></li> <li><i>A</i> ∩ <i>B</i>  je podskup skupa  <i>A</i></li> <li><i>A</i> ∩ <i>A</i>   =   <i>A</i></li> <li><i>A</i> ∩ ø   =   ø</li></ul></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Komplementi">Komplementi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=9" title="Uredi odlomak: Komplementi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=9" title="Uredi kôd odjeljka Komplementi"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135" /><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Komplement_skupa" title="Komplement skupa">Komplement skupa</a></div></i></div> <p>Dva se skupa također mogu "oduzeti". <b>Relativni komplement</b> skupa <i>A</i> u skupu <i>B</i> (još se koristi i naziv <b>skupovna razlika</b> skupova <i>B</i> i <i>A</i>), označeno s <i>B</i> − <i>A</i>, (ili <i>B</i> \ <i>A</i>), je skup svih elemenata koji su članovi skupa <i>B</i>, ali nisu članovi skupa <i>A</i>. Potrebno je uočiti da je valjana operacija "oduzimanja" članova koji nisu u skupu, poput micanja elementa <i>zelena</i> iz skupa {1,2,3} - takva operacija nema učinka. </p><p>U određenim postavkama, svi skupovi koji se promatraju, smatraju se podskupovima nekog danog <b>univerzalnog skupa</b> <i>U</i>. U takvim slučajevima, <i>U</i> − <i>A</i> zove se <b>apsolutni komplement</b> ili jednostavno <b>komplement</b> skupa <i>A</i>, i označava s <i>A</i>′, <i>A</i><sup>C</sup> ili <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 {\bar {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c003b99422260ba7cc644d36c04448c181a3759" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.676ex;" alt="{\displaystyle {\bar {A}}}" /></span>. </p> <div style="float:right;margin:1em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/Datoteka:Venn_B_minus_A.png" class="mw-file-description" title="B minus A"><img alt="B minus A" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Venn_B_minus_A.png/250px-Venn_B_minus_A.png" decoding="async" width="150" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/1/1b/Venn_B_minus_A.png 2x" data-file-width="294" data-file-height="209" /></a><figcaption>B minus A</figcaption></figure><center><small><b>Relativni komplement</b><br />skupa <i>A</i> u skupu <i>B</i></small></center> <figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/Datoteka:Venn_A_complement.png" class="mw-file-description" title="A complement"><img alt="A complement" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Venn_A_complement.png/250px-Venn_A_complement.png" decoding="async" width="150" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/5/5f/Venn_A_complement.png 2x" data-file-width="294" data-file-height="210" /></a><figcaption>A complement</figcaption></figure><center><small><b>Komplement</b> skupa <i>A</i> u skupu <i>U</i></small></center></div> <p>Primjeri: </p> <dl><dd><ul><li>{1, 2} − {crvena, bijela} = {1, 2}</li> <li>{1, 2, zelena} − {crvena, bijela, zelena} = {1, 2}</li> <li>{1, 2} − {1, 2} = ø</li> <li>Ako je <i>U</i> skup svih cijelih brojeva, <i>P</i> skup parnih brojeva, a <i>N</i> skup svih neparnih brojeva, tada komplement skupa <i>P</i> u <i>U</i> iznosi <i>N</i>, ili ekvivalentno, <i>P</i>′ = <i>N</i>.</li></ul></dd></dl> <p>Neka osnovna svojstva komplementa: </p> <dl><dd><ul><li><i>A</i> U <i>A′</i> = <i>U</i></li> <li><i>A</i> ∩ <i>A′</i> = ø</li> <li>(<i>A′ </i>)′ = <i>A</i></li> <li><i>A</i> − <i>A</i> = ø</li> <li><i>A</i> − <i>B</i> = <i>A</i> ∩ <i>B′</i></li></ul></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skup&veaction=edit&section=10" title="Uredi odlomak: Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skup&action=edit&section=10" title="Uredi kôd odjeljka Izvori"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6541845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r7012897">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"»""«"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20191219215513/https://web.math.pmf.unizg.hr/nastava/em/EM1/materijali/em1-skripta.pdf"><i>Elementarna matematika I</i></a> <span class="cs1-format">(PDF)</span>. Prirodoslovno-matematički fakultet. Zagreb. 2018. Inačica izvorne stranice arhivirana 19. prosinca 2019<span class="reference-accessdate">. Pristupljeno 8. travnja 2021.</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elementarna+matematika+I&rft.place=Zagreb&rft.pub=Prirodoslovno-matemati%C4%8Dki+fakultet&rft.date=2018&rft_id=https%3A%2F%2Fweb.math.pmf.unizg.hr%2Fnastava%2Fem%2FEM1%2Fmaterijali%2Fem1-skripta.pdf&rfr_id=info%3Asid%2Fhr.wikipedia.org%3ASkup" class="Z3988"></span><span class="cs1-maint citation-comment">CS1 održavanje: bot: nepoznat status originalnog URL-a (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_bot:_nepoznat_status_originalnog_URL-a" title="Kategorija:CS1 održavanje: bot: nepoznat status originalnog URL-a">link</a>)</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7012897" /><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20190724174822/https://www.math.pmf.unizg.hr/sites/default/files/pictures/ts-skripta-2015.pdf"><i>Teorija skupova</i></a> <span class="cs1-format">(PDF)</span>. Sveučilište u Zagrebu. Siječanj 2015. Inačica <a rel="nofollow" class="external text" href="https://www.math.pmf.unizg.hr/sites/default/files/pictures/ts-skripta-2015.pdf">izvorne stranice</a> <span class="cs1-format">(PDF)</span> arhivirana 24. srpnja 2019<span class="reference-accessdate">. Pristupljeno 24. listopada 2020.</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Teorija+skupova&rft.pub=Sveu%C4%8Dili%C5%A1te+u+Zagrebu&rft.date=2015-01&rft_id=https%3A%2F%2Fwww.math.pmf.unizg.hr%2Fsites%2Fdefault%2Ffiles%2Fpictures%2Fts-skripta-2015.pdf&rfr_id=info%3Asid%2Fhr.wikipedia.org%3ASkup" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7012897" /><cite id="CITEREFHalmos,_Paul_R._(Paul_Richard),_1916-2006," class="citation book cs1">Halmos, Paul R. (Paul Richard), 1916-2006,. <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/947951"><i>Naive set theory</i></a>. New York. <a href="/wiki/ISBN" class="mw-redirect" title="ISBN">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/0-387-90092-6" title="Posebno:Traži ISBN/0-387-90092-6"><bdi>0-387-90092-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Naive+set+theory&rft.place=New+York&rft.isbn=0-387-90092-6&rft.au=Halmos%2C+Paul+R.+%28Paul+Richard%29%2C+1916-2006%2C&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F947951&rfr_id=info%3Asid%2Fhr.wikipedia.org%3ASkup" class="Z3988"></span><span class="cs1-maint citation-comment">CS1 održavanje: dodatna interpunkcija (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_dodatna_interpunkcija" title="Kategorija:CS1 održavanje: dodatna interpunkcija">link</a>) CS1 održavanje: više imena: authors list (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_vi%C5%A1e_imena:_authors_list" title="Kategorija:CS1 održavanje: više imena: authors list">link</a>)</span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7012897" /><cite id="CITEREFStoll,_Robert_Roth" class="citation book cs1">Stoll, Robert Roth. 1979, ©1963. <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/5950625"><i>Set theory and logic</i></a>. Dover Publications. New York. <a href="/wiki/ISBN" class="mw-redirect" title="ISBN">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/0-486-63829-4" title="Posebno:Traži ISBN/0-486-63829-4"><bdi>0-486-63829-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Set+theory+and+logic&rft.place=New+York&rft.pub=Dover+Publications&rft.isbn=0-486-63829-4&rft.au=Stoll%2C+Robert+Roth.&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F5950625&rfr_id=info%3Asid%2Fhr.wikipedia.org%3ASkup" class="Z3988"></span> <span class="cs1-visible-error error citation-comment">Provjerite vrijednost datuma u parametru: <code class="cs1-code">|date=</code> (<a href="/wiki/Pomo%C4%87:CS1_gre%C5%A1ke#bad_date" title="Pomoć:CS1 greške">pomoć</a>)</span></span> </li> <li id="cite_note-Allenby-5"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Allenby_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Allenby_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7012897" /><cite id="CITEREFAllenby,_R._B._J._T.,1991" class="citation book cs1">Allenby, R. B. J. T.,. 1991. <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/26552538"><i>Rings, fields, and groups : an introduction to abstract algebra</i></a>. 2nd ed izdanje. E. Arnold. London. <a href="/wiki/ISBN" class="mw-redirect" title="ISBN">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/978-0-340-54440-2" title="Posebno:Traži ISBN/978-0-340-54440-2"><bdi>978-0-340-54440-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Rings%2C+fields%2C+and+groups+%3A+an+introduction+to+abstract+algebra&rft.place=London&rft.edition=2nd+ed&rft.pub=E.+Arnold&rft.date=1991&rft.isbn=978-0-340-54440-2&rft.au=Allenby%2C+R.+B.+J.+T.%2C&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F26552538&rfr_id=info%3Asid%2Fhr.wikipedia.org%3ASkup" class="Z3988"></span> <span class="cs1-visible-error error citation-comment"><span class="cs1-visible-error error citation-comment"><code class="cs1-code">|edition=</code> sadrži dodatni tekst (<a href="/wiki/Pomo%C4%87:CS1_gre%C5%A1ke#extra_text_edition" title="Pomoć:CS1 greške">pomoć</a>)</span></span><span class="cs1-maint citation-comment">CS1 održavanje: dodatna interpunkcija (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_dodatna_interpunkcija" title="Kategorija:CS1 održavanje: dodatna interpunkcija">link</a>) CS1 održavanje: više imena: authors list (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_vi%C5%A1e_imena:_authors_list" title="Kategorija:CS1 održavanje: više imena: authors list">link</a>)</span></span> </li> </ol></div></div>    </div><noscript><img src="https://auth.wikimedia.org/loginwiki/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Dobavljeno iz "<a dir="ltr" href="https://hr.wikipedia.org/w/index.php?title=Skup&oldid=6434982">https://hr.wikipedia.org/w/index.php?title=Skup&oldid=6434982</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorija</a>: <ul><li><a href="/wiki/Kategorija:Teorija_skupova" title="Kategorija:Teorija skupova">Teorija skupova</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skrivene kategorije: <ul><li><a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_bot:_nepoznat_status_originalnog_URL-a" title="Kategorija:CS1 održavanje: bot: nepoznat status originalnog URL-a">CS1 održavanje: bot: nepoznat status originalnog URL-a</a></li><li><a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_dodatna_interpunkcija" title="Kategorija:CS1 održavanje: dodatna interpunkcija">CS1 održavanje: dodatna interpunkcija</a></li><li><a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_vi%C5%A1e_imena:_authors_list" title="Kategorija:CS1 održavanje: više imena: authors list">CS1 održavanje: više imena: authors list</a></li><li><a href="/wiki/Kategorija:CS1_gre%C5%A1ke:_datumi" title="Kategorija:CS1 greške: datumi">CS1 greške: datumi</a></li><li><a href="/wiki/Kategorija:CS1_gre%C5%A1ke:_dodatni_tekst:_edition" title="Kategorija:CS1 greške: dodatni tekst: edition">CS1 greške: dodatni tekst: edition</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"> Ova stranica posljednji je put uređivana 31. srpnja 2022. u 01:19.</li> <li id="footer-info-copyright">Tekst je dostupan pod licencijom <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.hr">Creative Commons: Imenuj autora/Dijeli pod istim uvjetima</a>; mogu se primjenjivati i dodatni uvjeti. 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href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>103 jezika</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon 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