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[o]" accesskey="o" class=""><span>ಲಾಗ್ ಇನ್</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="More options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="ವೈಯಕ್ತಿಕ ಉಪಕರಣಗಳು" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">ವೈಯಕ್ತಿಕ ಉಪಕರಣಗಳು</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=kn.wikipedia.org&uselang=kn"><span>ದೇಣಿಗೆ</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:CreateAccount&returnto=%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" title="ನೀವು ಹೊಸ ಖಾತೆಯನ್ನು ತೆರೆದು ಲಾಗಿನ್ ಆಗುವುದನ್ನು ಹುರಿದುಂಬಿಸುತ್ತೇವೆ; ಆದಾಗ್ಯೂ, ಇದು ಅವಶ್ಯವೇನಲ್ಲ"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>ಹೊಸ ಖಾತೆ ತೆರೆಯಿರಿ</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:UserLogin&returnto=%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" title="ನೀವು ಲಾಗ್ ಇನ್ ಆಗಬೇಕೆಂದು ಕೋರುತ್ತೇವೆ, ಆದರೆ ಅದು ಖಡ್ಡಾಯ ಎನೂ ಅಲ್ಲ. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>ಲಾಗ್ ಇನ್</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> ಲಾಗ್ ಔಟ್ ಆದ ಸಂಪಾದಕರಿಗೆ ಪುಟಗಳು <a href="/wiki/%E0%B2%B8%E0%B2%B9%E0%B2%BE%E0%B2%AF:Introduction" aria-label="Learn more about editing"><span>ಹೆಚ್ಚಿನ ಮಾಹಿತಿ</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>ಕಾಣಿಕೆಗಳು</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:MyTalk" title="ಈ ip ವಿಳಾಸದಿಂದ ಮಾಡಲಾದ ಸಂಪಾದನೆಗಳ ಬಗ್ಗೆ ಚರ್ಚೆ [n]" accesskey="n"><span>IP ಚರ್ಚಾಪುಟ</span></a></li> </ul> </div> </div> </div> </div> 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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">ಪರಿವಿಡಿ</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ಮರೆ ಮಾಡಿ</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">ಮುನ್ನುಡಿ</div> </a> </li> <li id="toc-ಸದಸ್ಯತ್ವ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ಸದಸ್ಯತ್ವ"> <div class="vector-toc-text"> <span class="vector-toc-numb">೧</span> <span>ಸದಸ್ಯತ್ವ</span> </div> </a> <ul id="toc-ಸದಸ್ಯತ್ವ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ಸಂಖ್ಯತ್ವ_ಮತ್ತು_ಗಾತ್ರ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ಸಂಖ್ಯತ್ವ_ಮತ್ತು_ಗಾತ್ರ"> <div class="vector-toc-text"> <span class="vector-toc-numb">೨</span> <span>ಸಂಖ್ಯತ್ವ ಮತ್ತು ಗಾತ್ರ</span> </div> </a> <ul id="toc-ಸಂಖ್ಯತ್ವ_ಮತ್ತು_ಗಾತ್ರ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ಉಪಗಣ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ಉಪಗಣ"> <div class="vector-toc-text"> <span class="vector-toc-numb">೩</span> <span>ಉಪಗಣ</span> </div> </a> <ul id="toc-ಉಪಗಣ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ಮೂಲಭೂತ_ಪರಿಕರ್ಮಗಳು" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ಮೂಲಭೂತ_ಪರಿಕರ್ಮಗಳು"> <div class="vector-toc-text"> <span class="vector-toc-numb">೪</span> <span>ಮೂಲಭೂತ ಪರಿಕರ್ಮಗಳು</span> </div> </a> <ul id="toc-ಮೂಲಭೂತ_ಪರಿಕರ್ಮಗಳು-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ಉಲ್ಲೇಖಗಳು" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ಉಲ್ಲೇಖಗಳು"> <div class="vector-toc-text"> <span class="vector-toc-numb">೫</span> <span>ಉಲ್ಲೇಖಗಳು</span> </div> </a> <ul id="toc-ಉಲ್ಲೇಖಗಳು-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="ಪರಿವಿಡಿ" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " 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aria-label="ಇನ್ನೊಂದು ಭಾಷೆಯ ಲೇಖನಕ್ಕೆ ಹೋಗಿ. ೧೦೨ ಭಾಷೆಗಳಲ್ಲಿ ಲಭ್ಯವಿದೆ" > <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-102" 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">೧೦೨ ಭಾಷೆಗಳು</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) – ಸ್ವಿಸ್ ಜರ್ಮನ್" lang="gsw" hreflang="gsw" data-title="Menge (Mathematik)" data-language-autonym="Alemannisch" data-language-local-name="ಸ್ವಿಸ್ ಜರ್ಮನ್" 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 – ಅಂಹರಿಕ್" lang="am" hreflang="am" data-title="ስብስብ" data-language-autonym="አማርኛ" data-language-local-name="ಅಂಹರಿಕ್" 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) – ಅರೇಬಿಕ್" lang="ar" hreflang="ar" data-title="مجموعة (رياضيات)" data-language-autonym="العربية" data-language-local-name="ಅರೇಬಿಕ್" 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 – ಆಸ್ಟುರಿಯನ್" lang="ast" hreflang="ast" data-title="Conxuntu" data-language-autonym="Asturianu" data-language-local-name="ಆಸ್ಟುರಿಯನ್" 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 – ಅಜೆರ್ಬೈಜಾನಿ" lang="az" hreflang="az" data-title="Çoxluqlar" data-language-autonym="Azərbaycanca" data-language-local-name="ಅಜೆರ್ಬೈಜಾನಿ" 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 – ಬಶ್ಕಿರ್" lang="ba" hreflang="ba" data-title="Күмәклек" data-language-autonym="Башҡортса" data-language-local-name="ಬಶ್ಕಿರ್" 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 – ಬೆಲರೂಸಿಯನ್" lang="be" hreflang="be" data-title="Мноства" data-language-autonym="Беларуская" data-language-local-name="ಬೆಲರೂಸಿಯನ್" 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 – ಬಲ್ಗೇರಿಯನ್" lang="bg" hreflang="bg" data-title="Множество" data-language-autonym="Български" data-language-local-name="ಬಲ್ಗೇರಿಯನ್" 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 – ಬಾಂಗ್ಲಾ" lang="bn" hreflang="bn" data-title="সেট" data-language-autonym="বাংলা" data-language-local-name="ಬಾಂಗ್ಲಾ" 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) – ಬೋಸ್ನಿಯನ್" lang="bs" hreflang="bs" data-title="Skup (matematika)" data-language-autonym="Bosanski" data-language-local-name="ಬೋಸ್ನಿಯನ್" 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 – ಕೆಟಲಾನ್" lang="ca" hreflang="ca" data-title="Conjunt" data-language-autonym="Català" data-language-local-name="ಕೆಟಲಾನ್" 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) – ಮಧ್ಯ ಕುರ್ದಿಶ್" lang="ckb" hreflang="ckb" data-title="کۆمەڵە (ماتماتیک)" data-language-autonym="کوردی" data-language-local-name="ಮಧ್ಯ ಕುರ್ದಿಶ್" 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 – ಜೆಕ್" lang="cs" hreflang="cs" data-title="Množina" data-language-autonym="Čeština" data-language-local-name="ಜೆಕ್" 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 – ಚುವಾಶ್" lang="cv" hreflang="cv" data-title="Йыш" data-language-autonym="Чӑвашла" data-language-local-name="ಚುವಾಶ್" 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) – ವೆಲ್ಶ್" lang="cy" hreflang="cy" data-title="Set (mathemateg)" data-language-autonym="Cymraeg" data-language-local-name="ವೆಲ್ಶ್" 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 – ಡ್ಯಾನಿಶ್" lang="da" hreflang="da" data-title="Mængde" data-language-autonym="Dansk" data-language-local-name="ಡ್ಯಾನಿಶ್" 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) – ಜರ್ಮನ್" lang="de" hreflang="de" data-title="Menge (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="ಜರ್ಮನ್" 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 – ಗ್ರೀಕ್" lang="el" hreflang="el" data-title="Σύνολο" data-language-autonym="Ελληνικά" data-language-local-name="ಗ್ರೀಕ್" 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) – ಇಂಗ್ಲಿಷ್" lang="en" hreflang="en" data-title="Set (mathematics)" data-language-autonym="English" data-language-local-name="ಇಂಗ್ಲಿಷ್" 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) – ಎಸ್ಪೆರಾಂಟೊ" lang="eo" hreflang="eo" data-title="Aro (matematiko)" data-language-autonym="Esperanto" data-language-local-name="ಎಸ್ಪೆರಾಂಟೊ" 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 – ಸ್ಪ್ಯಾನಿಷ್" lang="es" hreflang="es" data-title="Conjunto" data-language-autonym="Español" data-language-local-name="ಸ್ಪ್ಯಾನಿಷ್" 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 – ಎಸ್ಟೊನಿಯನ್" lang="et" hreflang="et" data-title="Hulk" data-language-autonym="Eesti" data-language-local-name="ಎಸ್ಟೊನಿಯನ್" 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 – ಬಾಸ್ಕ್" lang="eu" hreflang="eu" data-title="Multzo" data-language-autonym="Euskara" data-language-local-name="ಬಾಸ್ಕ್" 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) – ಪರ್ಶಿಯನ್" lang="fa" hreflang="fa" data-title="مجموعه (ریاضیات)" data-language-autonym="فارسی" data-language-local-name="ಪರ್ಶಿಯನ್" 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 – ಫಿನ್ನಿಶ್" lang="fi" hreflang="fi" data-title="Joukko" data-language-autonym="Suomi" data-language-local-name="ಫಿನ್ನಿಶ್" 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-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ensemble" title="Ensemble – ಫ್ರೆಂಚ್" lang="fr" hreflang="fr" data-title="Ensemble" data-language-autonym="Français" data-language-local-name="ಫ್ರೆಂಚ್" 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 – ಫ್ರಿಯುಲಿಯನ್" lang="fur" hreflang="fur" data-title="Insiemi" data-language-autonym="Furlan" data-language-local-name="ಫ್ರಿಯುಲಿಯನ್" 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 – ಐರಿಷ್" lang="ga" hreflang="ga" data-title="Tacar" data-language-autonym="Gaeilge" data-language-local-name="ಐರಿಷ್" 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 – ಗಾನ್ ಚೀನೀಸ್" lang="gan" hreflang="gan" data-title="集合" data-language-autonym="贛語" data-language-local-name="ಗಾನ್ ಚೀನೀಸ್" 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 – ಸ್ಕಾಟಿಶ್ ಗೆಲಿಕ್" lang="gd" hreflang="gd" data-title="Seata" data-language-autonym="Gàidhlig" data-language-local-name="ಸ್ಕಾಟಿಶ್ ಗೆಲಿಕ್" 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 – ಗ್ಯಾಲಿಶಿಯನ್" lang="gl" hreflang="gl" data-title="Conxunto" data-language-autonym="Galego" data-language-local-name="ಗ್ಯಾಲಿಶಿಯನ್" 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) – ಹೀಬ್ರೂ" lang="he" hreflang="he" data-title="קבוצה (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="ಹೀಬ್ರೂ" 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) – ಹಿಂದಿ" lang="hi" hreflang="hi" data-title="समुच्चय (गणित)" data-language-autonym="हिन्दी" data-language-local-name="ಹಿಂದಿ" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Skup" title="Skup – ಕ್ರೊಯೇಶಿಯನ್" lang="hr" hreflang="hr" data-title="Skup" data-language-autonym="Hrvatski" data-language-local-name="ಕ್ರೊಯೇಶಿಯನ್" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Halmaz_(matematika)" title="Halmaz (matematika) – ಹಂಗೇರಿಯನ್" lang="hu" hreflang="hu" data-title="Halmaz (matematika)" data-language-autonym="Magyar" data-language-local-name="ಹಂಗೇರಿಯನ್" 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 – ಅರ್ಮೇನಿಯನ್" lang="hy" hreflang="hy" data-title="Բազմություն" data-language-autonym="Հայերեն" data-language-local-name="ಅರ್ಮೇನಿಯನ್" 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 – ಇಂಟರ್‌ಲಿಂಗ್ವಾ" lang="ia" hreflang="ia" data-title="Insimul" data-language-autonym="Interlingua" data-language-local-name="ಇಂಟರ್‌ಲಿಂಗ್ವಾ" 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) – ಇಂಡೋನೇಶಿಯನ್" lang="id" hreflang="id" data-title="Himpunan (matematika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="ಇಂಡೋನೇಶಿಯನ್" 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 – ಇಡೊ" lang="io" hreflang="io" data-title="Ensemblo" data-language-autonym="Ido" data-language-local-name="ಇಡೊ" 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 – ಐಸ್‌ಲ್ಯಾಂಡಿಕ್" lang="is" hreflang="is" data-title="Mengi" data-language-autonym="Íslenska" data-language-local-name="ಐಸ್‌ಲ್ಯಾಂಡಿಕ್" 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 – ಇಟಾಲಿಯನ್" lang="it" hreflang="it" data-title="Insieme" data-language-autonym="Italiano" data-language-local-name="ಇಟಾಲಿಯನ್" 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 – ಜಾಪನೀಸ್" lang="ja" hreflang="ja" data-title="集合" data-language-autonym="日本語" data-language-local-name="ಜಾಪನೀಸ್" 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 – ಜಾರ್ಜಿಯನ್" lang="ka" hreflang="ka" data-title="სიმრავლე" data-language-autonym="ქართული" data-language-local-name="ಜಾರ್ಜಿಯನ್" 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 – ಕಝಕ್" lang="kk" hreflang="kk" data-title="Бөлік" data-language-autonym="Қазақша" data-language-local-name="ಕಝಕ್" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A7%91%ED%95%A9" title="집합 – ಕೊರಿಯನ್" lang="ko" hreflang="ko" data-title="집합" data-language-autonym="한국어" data-language-local-name="ಕೊರಿಯನ್" 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 – ಕುರ್ದಿಷ್" lang="ku" hreflang="ku" data-title="Kom" data-language-autonym="Kurdî" data-language-local-name="ಕುರ್ದಿಷ್" 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 – ಲ್ಯಾಟಿನ್" lang="la" hreflang="la" data-title="Copia" data-language-autonym="Latina" data-language-local-name="ಲ್ಯಾಟಿನ್" 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 – Lombard" lang="lmo" hreflang="lmo" data-title="Insemma" data-language-autonym="Lombard" data-language-local-name="Lombard" 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 – ಲಿಂಗಾಲ" lang="ln" hreflang="ln" data-title="Elɔngɔ́tɛ̂ lisangá" data-language-autonym="Lingála" data-language-local-name="ಲಿಂಗಾಲ" 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 – ಲಿಥುವೇನಿಯನ್" lang="lt" hreflang="lt" data-title="Aibė" data-language-autonym="Lietuvių" data-language-local-name="ಲಿಥುವೇನಿಯನ್" 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 – ಲಾಟ್ವಿಯನ್" lang="lv" hreflang="lv" data-title="Kopa" data-language-autonym="Latviešu" data-language-local-name="ಲಾಟ್ವಿಯನ್" 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 – ಮೆಸಿಡೋನಿಯನ್" lang="mk" hreflang="mk" data-title="Множество" data-language-autonym="Македонски" data-language-local-name="ಮೆಸಿಡೋನಿಯನ್" 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) – ಮಲಯಾಳಂ" lang="ml" hreflang="ml" data-title="ഗണം (ഗണിതം)" data-language-autonym="മലയാളം" data-language-local-name="ಮಲಯಾಳಂ" 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 – ಮಂಗೋಲಿಯನ್" lang="mn" hreflang="mn" data-title="Олонлог" data-language-autonym="Монгол" data-language-local-name="ಮಂಗೋಲಿಯನ್" 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 – ಮಲಯ್" lang="ms" hreflang="ms" data-title="Set" data-language-autonym="Bahasa Melayu" data-language-local-name="ಮಲಯ್" 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 – ಬರ್ಮೀಸ್" lang="my" hreflang="my" data-title="အစု" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="ಬರ್ಮೀಸ್" 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 – ಎರ್ಝ್ಯಾ" lang="myv" hreflang="myv" data-title="Вейссаевкс" data-language-autonym="Эрзянь" data-language-local-name="ಎರ್ಝ್ಯಾ" 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) – ಲೋ ಜರ್ಮನ್" lang="nds" hreflang="nds" data-title="Koppel (Mathematik)" data-language-autonym="Plattdüütsch" data-language-local-name="ಲೋ ಜರ್ಮನ್" 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) – ಡಚ್" lang="nl" hreflang="nl" data-title="Verzameling (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="ಡಚ್" 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 – ನಾರ್ವೇಜಿಯನ್ ನೈನಾರ್ಸ್ಕ್" lang="nn" hreflang="nn" data-title="Mengd" data-language-autonym="Norsk nynorsk" data-language-local-name="ನಾರ್ವೇಜಿಯನ್ ನೈನಾರ್ಸ್ಕ್" 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 – ನಾರ್ವೆಜಿಯನ್ ಬೊಕ್ಮಲ್" lang="nb" hreflang="nb" data-title="Mengde" data-language-autonym="Norsk bokmål" data-language-local-name="ನಾರ್ವೆಜಿಯನ್ ಬೊಕ್ಮಲ್" 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 – ಒಸಿಟನ್" lang="oc" hreflang="oc" data-title="Ensemble" data-language-autonym="Occitan" data-language-local-name="ಒಸಿಟನ್" 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) – ಪಂಜಾಬಿ" lang="pa" hreflang="pa" data-title="ਸੈੱਟ (ਗਣਿਤ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="ಪಂಜಾಬಿ" 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 – ಪೊಲಿಶ್" lang="pl" hreflang="pl" data-title="Zbiór" data-language-autonym="Polski" data-language-local-name="ಪೊಲಿಶ್" 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 – ಪೋರ್ಚುಗೀಸ್" lang="pt" hreflang="pt" data-title="Conjunto" data-language-autonym="Português" data-language-local-name="ಪೋರ್ಚುಗೀಸ್" 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 – ಕ್ವೆಚುವಾ" lang="qu" hreflang="qu" data-title="Tantachisqa" data-language-autonym="Runa Simi" data-language-local-name="ಕ್ವೆಚುವಾ" 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 – ರೊಮೇನಿಯನ್" lang="ro" hreflang="ro" data-title="Mulțime" data-language-autonym="Română" data-language-local-name="ರೊಮೇನಿಯನ್" 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 – ರಷ್ಯನ್" lang="ru" hreflang="ru" data-title="Множество" data-language-autonym="Русский" data-language-local-name="ರಷ್ಯನ್" 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 – ಸಿಸಿಲಿಯನ್" lang="scn" hreflang="scn" data-title="Nzemi" data-language-autonym="Sicilianu" data-language-local-name="ಸಿಸಿಲಿಯನ್" 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 – ಸರ್ಬೋ-ಕ್ರೊಯೇಶಿಯನ್" lang="sh" hreflang="sh" data-title="Skup" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="ಸರ್ಬೋ-ಕ್ರೊಯೇಶಿಯನ್" 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 – ಸ್ಲೋವಾಕ್" lang="sk" hreflang="sk" data-title="Množina" data-language-autonym="Slovenčina" data-language-local-name="ಸ್ಲೋವಾಕ್" 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 – ಸ್ಲೋವೇನಿಯನ್" lang="sl" hreflang="sl" data-title="Množica" data-language-autonym="Slovenščina" data-language-local-name="ಸ್ಲೋವೇನಿಯನ್" 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) – ಸೊಮಾಲಿ" lang="so" hreflang="so" data-title="Qaybta (xisaab)" data-language-autonym="Soomaaliga" data-language-local-name="ಸೊಮಾಲಿ" 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 – ಅಲ್ಬೇನಿಯನ್" lang="sq" hreflang="sq" data-title="Bashkësitë" data-language-autonym="Shqip" data-language-local-name="ಅಲ್ಬೇನಿಯನ್" 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 – ಸೆರ್ಬಿಯನ್" lang="sr" hreflang="sr" data-title="Скуп" data-language-autonym="Српски / srpski" data-language-local-name="ಸೆರ್ಬಿಯನ್" 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 – ಸ್ವೀಡಿಷ್" lang="sv" hreflang="sv" data-title="Mängd" data-language-autonym="Svenska" data-language-local-name="ಸ್ವೀಡಿಷ್" 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) – Silesian" lang="szl" hreflang="szl" data-title="Mynga (matymatyka)" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%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) – ತಮಿಳು" lang="ta" hreflang="ta" data-title="கணம் (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="ತಮಿಳು" 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 – ತೆಲುಗು" lang="te" hreflang="te" data-title="సమితులు" data-language-autonym="తెలుగు" data-language-local-name="ತೆಲುಗು" 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) – ಥಾಯ್" lang="th" hreflang="th" data-title="เซต (คณิตศาสตร์)" data-language-autonym="ไทย" data-language-local-name="ಥಾಯ್" 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) – ಟ್ಯಾಗಲೋಗ್" lang="tl" hreflang="tl" data-title="Pangkat (matematika)" data-language-autonym="Tagalog" data-language-local-name="ಟ್ಯಾಗಲೋಗ್" 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 – ಟರ್ಕಿಶ್" lang="tr" hreflang="tr" data-title="Küme" data-language-autonym="Türkçe" data-language-local-name="ಟರ್ಕಿಶ್" 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 – ಉಕ್ರೇನಿಯನ್" lang="uk" hreflang="uk" data-title="Множина" data-language-autonym="Українська" data-language-local-name="ಉಕ್ರೇನಿಯನ್" 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) – ಉರ್ದು" lang="ur" hreflang="ur" data-title="طاقم (ریاضی)" data-language-autonym="اردو" data-language-local-name="ಉರ್ದು" 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) – ಉಜ್ಬೇಕ್" lang="uz" hreflang="uz" data-title="Toʻplam (matematika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ಉಜ್ಬೇಕ್" 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) – ವಿಯೆಟ್ನಾಮೀಸ್" lang="vi" hreflang="vi" data-title="Tập hợp (toán học)" data-language-autonym="Tiếng Việt" data-language-local-name="ವಿಯೆಟ್ನಾಮೀಸ್" 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） – ವು ಚೈನೀಸ್" lang="wuu" hreflang="wuu" data-title="集合（数学）" data-language-autonym="吴语" data-language-local-name="ವು ಚೈನೀಸ್" 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 – ಕಲ್ಮೈಕ್" lang="xal" hreflang="xal" data-title="Олн" data-language-autonym="Хальмг" data-language-local-name="ಕಲ್ಮೈಕ್" 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 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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 – ನಾನ್" lang="nan" hreflang="nan" data-title="Chi̍p-ha̍p" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="ನಾನ್" 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 – ಕ್ಯಾಂಟನೀಸ್" lang="yue" hreflang="yue" data-title="集合" data-language-autonym="粵語" data-language-local-name="ಕ್ಯಾಂಟನೀಸ್" 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="ಇತರ ಭಾಷಾ ಕೊಂಡಿಗಳನ್ನು ಸಂಪಾದಿಸು" class="wbc-editpage">ಕೊಂಡಿಗಳನ್ನು 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title="ಇಲ್ಲಿಗೆ ಸಂಪರ್ಕ ಹೊಂದಿರುವ ಎಲ್ಲಾ ವಿಕಿ ಪುಟಗಳ ಪಟ್ಟಿ [j]" accesskey="j"><span>ಇಲ್ಲಿಗೆ ಯಾವ ಸಂಪರ್ಕ ಕೂಡುತ್ತದೆ</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:RecentChangesLinked/%E0%B2%97%E0%B2%A3_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4)" rel="nofollow" title="ಈ ಪುಟದಿಂದ ಸಂಪರ್ಕ ಹೊಂದಿರುವ ಪುಟಗಳಲ್ಲಿನ ಇತ್ತೀಚಿನ ಬದಲಾವಣೆಗಳು [k]" accesskey="k"><span>ಸಂಬಂಧಪಟ್ಟ ಬದಲಾವಣೆಗಳು</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:SpecialPages" title="ಎಲ್ಲಾ ವಿಶೇಷ ಪುಟಗಳ ಪಟ್ಟಿ [q]" accesskey="q"><span>ವಿಶೇಷ ಪುಟಗಳು</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E0%B2%97%E0%B2%A3_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4)&oldid=1225362" title="ಪುಟದ ಈ ಆವೃತ್ತಿಗೆ ಶಾಶ್ವತ ಕೊಂಡಿ"><span>ಸ್ಥಿರ ಕೊಂಡಿ</span></a></li><li id="t-info" class="mw-list-item"><a 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typeof="mw:File/Thumb"><a href="/wiki/%E0%B2%9A%E0%B2%BF%E0%B2%A4%E0%B3%8D%E0%B2%B0:Example_of_a_set.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Example_of_a_set.svg/220px-Example_of_a_set.svg.png" decoding="async" width="220" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Example_of_a_set.svg/330px-Example_of_a_set.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Example_of_a_set.svg/440px-Example_of_a_set.svg.png 2x" data-file-width="450" data-file-height="400" /></a><figcaption>ಒಂದು ವೆನ್ ಚಿತ್ರದಲ್ಲಿ ಬಹುಕೋನಗಳ ಗಣ</figcaption></figure> <p>ಮೂಲಭೂತವಾಗಿ, <b>ಗಣ</b> ಎಂಬುದು ಸಮೂಹಗಳ ನಿರೂಪಣೆ. ಗಣವು ವಿಭಿನ್ನ ವಸ್ತುಗಳ ಸಂಗ್ರಹ.<sup id="cite_ref-JainAhmad1995_1-0" class="reference"><a href="#cite_note-JainAhmad1995-1"><span class="cite-bracket">[</span>೧<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Goldberg1986_2-0" class="reference"><a href="#cite_note-Goldberg1986-2"><span class="cite-bracket">[</span>೨<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CormenCormen2001_3-0" class="reference"><a href="#cite_note-CormenCormen2001-3"><span class="cite-bracket">[</span>೩<span class="cite-bracket">]</span></a></sup> <a href="/wiki/%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಗಣಿತ">ಗಣಿತ</a> ಮತ್ತು <a href="/wiki/%E0%B2%97%E0%B2%A3%E0%B2%95%E0%B2%AF%E0%B2%82%E0%B2%A4%E0%B3%8D%E0%B2%B0" class="mw-redirect" title="ಗಣಕಯಂತ್ರ">ಗಣಕಯಂತ್ರ</a> ಶಾಸ್ತ್ರದಲ್ಲಿ ಗಣ ಸಿದ್ಧಾಂತ (<a href="https://en.wikipedia.org/wiki/Set_theory" class="extiw" title="en:Set theory">Set Theory</a>) ಒಂದು ಪ್ರಮುಖವಾದ ವಿಷಯ. ಉದಾಹರಣೆಗಳು: W = {೦, ೧, ೨, ೩, ೪, ...} ಎಂಬುದು <a href="/wiki/%E0%B2%85%E0%B2%82%E0%B2%95%E0%B2%BF" title="ಅಂಕಿ">ಅಂಕಿಗಳ</a> ಒಂದು ಅನಂತ ಗಣವಾದರೆ (infinite set), ಪ = {ಹಸು, ಕಾಗೆ, ಕೋಳಿ, ಸಿಂಹ, ಹುಲಿ} ಎಂಬುದು, ೫ ಪ್ರಾಣಿ ಸದಸ್ಯಗಳ ಸಾಂತಗಣ, ವಾಸ್ತವ ಸರಳರೇಖೆಯ (line of real numbers) ಮೇಲಣ ಬಿಂದುಗಳ ಗಣ, (0,1) ಅಂತರದಲ್ಲಿ ವ್ಯಾಖ್ಯಿಸಿರುವ ವಾಸ್ತವ ಬೆಲೆಗಳುಳ್ಳ (real values) <a href="https://en.wikipedia.org/wiki/Continuous_function" class="extiw" title="en:Continuous function">ಅವಿಚ್ಛಿನ್ನ ಉತ್ಪನ್ನಗಳ</a> ಗಣ (set of continuous functions), ಗಣಗಳ ಗಣ (set of sets). ಸಾಮಾನ್ಯವಾಗಿ, ಗಣ ಎಂಬುದು ವಸ್ತು <i>ಮಾದರಿ</i> ಸಮೂಹಗಳ ನಿರೂಪಣೆಯೇ ಹೊರತು, ವಸ್ತು <i>ನಿದರ್ಶನ</i> ಗಳ ಸಮೂಹವಲ್ಲ. ಆದ್ದರಿಂದ, ಪ = {೨ ಹಸು, ೩ ಕಾಗೆ, ೫ ಕೋಳಿ, ೧ ಸಿಂಹ, ಹುಲಿ, ಹುಲಿ} ಎಂಬುದು ತಪ್ಪಾದ ನಿರೂಪಣೆ. ವಸ್ತು ನಿದರ್ಶನಗಳ ಸಮೂಹಗಳನ್ನು, ಆವಳಿ-ಗಣ (<a href="https://en.wikipedia.org/wiki/Multiset" class="extiw" title="en:Multiset">multi-set</a>) ಎಂದು ಕರೆಯಲಾಗುತ್ತದೆ. ಗಣಗಳ ಲಕ್ಷಣಗಳು ಆವಳಿ-ಗಣಗಳಿಗಿಂತ ವಿಭಿನ್ನವಾದುದು. </p><p>ಗಣಗಳ ನಿರೂಪಣೆ ಯಾವುದೇ ಅನ್ವಯವನ್ನು ಹೊಂದಿರುವುದಿಲ್ಲ. ಆದ್ದರಿಂದ {೨, ೪, ೬, ೮} ಮತ್ತು {೪, ೨, ೮, ೬} ಇವೆರಡು ಗಣಗಳೂ ಒಂದೆ.<sup id="cite_ref-MaurerRalston2005_4-0" class="reference"><a href="#cite_note-MaurerRalston2005-4"><span class="cite-bracket">[</span>೪<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_5-0" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>೫<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-DalenDoets2014_6-0" class="reference"><a href="#cite_note-DalenDoets2014-6"><span class="cite-bracket">[</span>೬<span class="cite-bracket">]</span></a></sup> ಸಾಮಾನ್ಯವಾಗಿ, ಗಣಗಳು <i>ಒಂದೇ ಮಾದರಿಯ</i> ವಸ್ತು ಸಮೂಹವನ್ನು ನಿರೂಪಿಸುತ್ತವೆ. ಆದ್ದರಿಂದ {೧, ೨, ೩, ಹಸು} ಎಂಬ ಗಣ ನಿರೂಪಣೆ, ಸಾಮಾನ್ಯವಾಗಿ ತಪ್ಪೆಂದು ಭಾವಿಸಲಾಗುತ್ತದೆ. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="ಸದಸ್ಯತ್ವ"><span id=".E0.B2.B8.E0.B2.A6.E0.B2.B8.E0.B3.8D.E0.B2.AF.E0.B2.A4.E0.B3.8D.E0.B2.B5"></span>ಸದಸ್ಯತ್ವ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B2%97%E0%B2%A3_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4)&action=edit&section=1" title="ವಿಭಾಗ ಸಂಪಾದಿಸಿ: ಸದಸ್ಯತ್ವ"><span>ಬದಲಾಯಿಸಿ</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/%E0%B2%9A%E0%B2%BF%E0%B2%A4%E0%B3%8D%E0%B2%B0:Venn_A_subset_B.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Venn_A_subset_B.svg/150px-Venn_A_subset_B.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Venn_A_subset_B.svg/225px-Venn_A_subset_B.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Venn_A_subset_B.svg/300px-Venn_A_subset_B.svg.png 2x" data-file-width="155" data-file-height="155" /></a><figcaption><div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><i>A</i> is a <b>subset</b> of <i>B</i></div></figcaption></figure> <p>ಯಾವುದೆ ಒಂದು ಗಣ U ನಲ್ಲಿ ಸೇರುವ ಎಲ್ಲಾ ವಸ್ತುಗಳೂ U ನ <b>ಸದಸ್ಯ</b>ಗಳು ಅಥವಾ <b>ಧಾತು</b>ಗಳೆಂದು ಕರೆಯಲ್ಪಡುತ್ತವೆ. a ∈ A ಎಂದರೆ a ಎಂಬ ವಸ್ತು A ಗಣದ ಒಂದು ಧಾತು. ಗಣದಲ್ಲಿ ಅನಂತ ಸದಸ್ಯರು ಇದ್ದಲ್ಲಿ, ಅದನ್ನು "ಅನಂತ ಗಣ"ವೆಂದೂ, ಇಲ್ಲವಾದರೆ, "ಸಾಂತಗಣ"ವೆಂದೂ ಹೇಳಲಾಗುತ್ತದೆ. ಗಣಗಳ ಸದಸ್ಯ ವಸ್ತುಗಳು, ತಾವೆ ಗಣಗಳಾಗಿರಬಹುದು. ಆದ್ದರಿಂದ {{೧,೨}, {೩,೪}} ಎಂಬುದು, ಎರಡು ಸದಸ್ಯರುಳ್ಳ ಗಣ. ಈ ಎರಡೂ ಸದಸ್ಯರು, ತಾವೇ ಗಣಗಳಾಗಿದ್ದು, ಎರಡರಲ್ಲೂ, ಪ್ರತ್ಯೇಕ ೨-ಸದಸ್ಯ ಗಣಗಳು ಇವೆ. ಸಾಮಾನ್ಯವಾಗಿ, ಗಣಗಳು ತಾವೇ ತಮ್ಮ ಸದಸ್ಯರಾಗಲು ಸಾಧ್ಯವಿಲ್ಲ. ಆದ್ದರಿಂದ ಪ = {{೧,೨}, {೩,೪}, ಪ} ಎಂಬುದು ತಪ್ಪಾದ ನಿರೂಪಣೆ. ಈ ಪ್ರಮಾಣವನ್ನು, ಅಡಿಪಾಯ ಆಧಾರ ಸೂತ್ರ (<a href="https://en.wikipedia.org/wiki/Axiom_of_regularity" class="extiw" title="en:Axiom of regularity">Axiom of Foundation</a>) ಎಂದು ಕರೆಯಲಾಗುತ್ತದೆ. ಇದು, <a href="https://en.wikipedia.org/wiki/Russell%27s_paradox" class="extiw" title="en:Russell's paradox">ರಸೆಲ್ ವಿರೋಧಾಭಾಸಗಳಂಥ</a> ಸನ್ನಿವೇಶಗಳನ್ನು ತಡೆಗಟ್ಟಲು ಸಹಾಯಕವಾಗಿರುವುದು. ಹಾಗಾಗಿಯೂ, ಇತ್ತೀಚಿಗೆ, ವಿರೋಧಾಭಾಸವಿಲ್ಲದೆಯೆ ಗಣಗಳಿಗೆ ಸ್ವ-ಸದಸ್ಯತ್ವವನ್ನು ನೀಡಬಹುದು ಎಂದು ನಿರೂಪಿಸಲಾಗಿದೆ. ಇಂತಹ ಗಣಗಳನ್ನು "ಸಾಧಾರವಿಲ್ಲದ" ಗಣಗಳೆಂದು (non-wellfounded sets) ಕರೆಯಲಾಗುತ್ತದೆ. </p> <div class="mw-heading mw-heading2"><h2 id="ಸಂಖ್ಯತ್ವ_ಮತ್ತು_ಗಾತ್ರ"><span id=".E0.B2.B8.E0.B2.82.E0.B2.96.E0.B3.8D.E0.B2.AF.E0.B2.A4.E0.B3.8D.E0.B2.B5_.E0.B2.AE.E0.B2.A4.E0.B3.8D.E0.B2.A4.E0.B3.81_.E0.B2.97.E0.B2.BE.E0.B2.A4.E0.B3.8D.E0.B2.B0"></span>ಸಂಖ್ಯತ್ವ ಮತ್ತು ಗಾತ್ರ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B2%97%E0%B2%A3_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4)&action=edit&section=2" title="ವಿಭಾಗ ಸಂಪಾದಿಸಿ: ಸಂಖ್ಯತ್ವ ಮತ್ತು ಗಾತ್ರ"><span>ಬದಲಾಯಿಸಿ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>ಯಾವುದೇ ಗಣ 'ಪ' ದಲ್ಲಿ ಎಷ್ಟು ಸದಸ್ಯರಿದ್ದಾರೋ ಅದೇ ಅದರ "ಸಂಖ್ಯತ್ವ" (cardinality).<sup id="cite_ref-Moschovakis1994_7-0" class="reference"><a href="#cite_note-Moschovakis1994-7"><span class="cite-bracket">[</span>೭<span class="cite-bracket">]</span></a></sup> ಪ-ಗಣದ ಸಂಖ್ಯತ್ವವನ್ನು |ಪ| ಎಂದು ಬರೆಯಲಾಗುತ್ತೆ. ಉದಾಹರಣೆಗೆ, ಪ ಎಂಬುದು {{೧,೨}, ೩, ೪, {೫,೬}} ಆದರೆ, |ಪ| = ೪. ಗಮನಿಸಿ, ಯಾವುದೇ ಗಣ <i>ಎ</i>, ಇನ್ನೊಂದು ಗಣ <i>ಪ</i> ದ ಸದಸ್ಯವಾದಲ್ಲಿ, ಪ-ಗಣದ ಸಂಖ್ಯತ್ವದ ಎಣಿಕೆಯಲ್ಲಿ <i>ಎ</i> ಅನ್ನು ಒಂದೇ ಬಾರಿ ಏಣಿಸಲಾಗುತ್ತೆ. <i>ಎ</i> ಎಂಬುದು ತಾನೇ ಒಂದು ಅನಂತ ಗಣವಾಗಿರಬಹುದು; ಆದರೆ, ಪ-ಸದಸ್ಯತ್ವದ ಪ್ರಕಾರ, <i>ಎ</i> ಎಂಬುದು ಒಂದೇ ಸದಸ್ಯ. <i>ಪ</i> ಮತ್ತು <i>ಮ</i> ಎಂಬ ಎರಡು ಗಣಗಳು ಇದ್ದಲ್ಲಿ, ಮತ್ತು <i>ಪ</i> ಗಣದ ಪ್ರತಿಯೊಂದು ಸದಸ್ಯರಿಗೂ <i>ಮ</i> ಗಣದಿಂದ ಏಕೈಕ ಸದಸ್ಯರನ್ನು ಆಯ್ಕೆ ಮಾಡುವಂತಾದಲ್ಲಿ, ಹಾಗೆಯೆ <i>ಮ</i> ಗಣದ ಪ್ರತಿಯೊಂದು ಸದಸ್ಯರಿಗೂ <i>ಪ</i> ಗಣದಿಂದ ಒಂದು ಏಕೈಕ ಸದಸ್ಯರನ್ನು ಆಯ್ಕೆ ಮಾಡುವಂತಾದಲ್ಲಿ, <i>ಪ</i> ಮತ್ತು <i>ಮ</i> ಗಣಗಳು "<i>ಸಮಗಾತ್ರ ಗಣ</i>"ಗಳೆಂದು ಹೇಳಲಾಗುತ್ತೆ<i>. </i>ಸಾಂತಗಣಗಳ ಗಾತ್ರಗಳನ್ನು ಅವುಗಳ ಸಂಖ್ಯತ್ವಗಳ ಮೂಲಕ ಸುಲಭವಾಗಿ ಹೋಲಿಸಬಹುದು. ಆದರೆ, ಅನಂತ ಗಣಗಳಿಗೆ ಇದು ಅಷ್ಟು ಸುಲಭವಲ್ಲ. ಉದಾಹರಣೆಗೆ, "<a href="/wiki/%E0%B2%B8%E0%B3%8D%E0%B2%B5%E0%B2%BE%E0%B2%AD%E0%B2%BE%E0%B2%B5%E0%B2%BF%E0%B2%95_%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B3%86" title="ಸ್ವಾಭಾವಿಕ ಸಂಖ್ಯೆ">ಸ್ವಾಭಾವಿಕ ಸಂಖ್ಯೆ</a>" (Natural numbers N) ನ = {೧, ೨, ೩, ...} ಮತ್ತು "<a href="https://en.wikipedia.org/wiki/Integer" class="extiw" title="en:Integer">ಪೂರ್ಣ ಸಂಖ್ಯೆ</a>" (Integers Z) ಜ಼ = {..., -೩, -೨, -೧, ೦, ೧, ೨, ೩, ...}, ಇವೆರಡೂ ಗಣಗಳ ಗಾತ್ರವೂ ಒಂದೆ. </p><p>ಪ್ರತಿಯೊಂದು ನೈತಿಕ ಸಂಖ್ಯೆಗೂ ಒಂದು ಏಕೈಕವಾದ ಪೂರ್ಣ ಸಂಖ್ಯೆಯನ್ನು ಆಯ್ಕೆ ಮಾಡಬಹುದು. ಹಾಗೆಯೇ, ಪ್ರತಿಯೊಂದು ಪೂರ್ಣ ಸಂಖ್ಯೆಗೂ ಒಂದು ಏಕೈಕವಾದ ನೈತಿಕ ಸಂಖ್ಯೆಯನ್ನು ಆಯ್ಕೆ ಮಾಡಬಹುದು. ಆದರೆ, "<a href="/wiki/%E0%B2%A8%E0%B3%88%E0%B2%9C_%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B3%86" title="ನೈಜ ಸಂಖ್ಯೆ">ವಾಸ್ತವ ಸಂಖ್ಯೆ</a>" (Real numbers R) ಗಣದ ಗಾತ್ರವು ನೈತಿಕಸಂಖ್ಯೆಗಳಿಗಿಂತ ದೊಡ್ಡದು! ಎಲ್ಲಾ ಅನಂತ ಗಣಗಳೂ ಒಂದೇ ಗಾತ್ರವಲ್ಲ ಎಂಬುದು ಗಣ ಸಿದ್ಧಾಂತದ ಒಂದು ಮಹತ್ವವಾದ ನಿರೂಪಣೆ. ಇದನ್ನು <a href="https://en.wikipedia.org/wiki/Georg_Cantor" class="extiw" title="en:Georg Cantor">ಗಿಯೋರ್ಗ್ ಕಾಂಟೋರ್‌ನ</a> <i>ಕರ್ಣ ವಾದ</i> (diagonal argument) ಎಂದು ಹೇಳಲಾಗುತ್ತೆ.<sup id="cite_ref-Cantor.1891_8-0" class="reference"><a href="#cite_note-Cantor.1891-8"><span class="cite-bracket">[</span>೮<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="ಉಪಗಣ"><span id=".E0.B2.89.E0.B2.AA.E0.B2.97.E0.B2.A3"></span>ಉಪಗಣ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B2%97%E0%B2%A3_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4)&action=edit&section=3" title="ವಿಭಾಗ ಸಂಪಾದಿಸಿ: ಉಪಗಣ"><span>ಬದಲಾಯಿಸಿ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>A</i> ⊆ <i>B</i> (ಅಥವಾ <i>B</i> ⊆ <i>A</i>) ಎಂದರೆ A ಗಣ B ಯ ಉಪಗಣ.<sup id="cite_ref-Hausdorff2005_9-0" class="reference"><a href="#cite_note-Hausdorff2005-9"><span class="cite-bracket">[</span>೯<span class="cite-bracket">]</span></a></sup> ಅಥವಾ A ಯ ಪ್ರತಿಯೊಂದು ಧಾತುವೂ B ಯ ಧಾತು. ವಿಶೇಷ ಸಂದರ್ಭವಾಗಿ, ಪ್ರತಿಯೊಂದು ಗಣವೂ ಅದರದೇ ಉಪಗಣ. <i>A</i> ⊆ <i>B</i> ಮತ್ತು <i>B</i> ⊆ <i>A</i> ಆದಾಗ ಮಾತ್ರ A = B.<sup id="cite_ref-Lucas1990_10-0" class="reference"><a href="#cite_note-Lucas1990-10"><span class="cite-bracket">[</span>೧೦<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="ಮೂಲಭೂತ_ಪರಿಕರ್ಮಗಳು"><span id=".E0.B2.AE.E0.B3.82.E0.B2.B2.E0.B2.AD.E0.B3.82.E0.B2.A4_.E0.B2.AA.E0.B2.B0.E0.B2.BF.E0.B2.95.E0.B2.B0.E0.B3.8D.E0.B2.AE.E0.B2.97.E0.B2.B3.E0.B3.81"></span>ಮೂಲಭೂತ ಪರಿಕರ್ಮಗಳು</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B2%97%E0%B2%A3_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4)&action=edit&section=4" title="ವಿಭಾಗ ಸಂಪಾದಿಸಿ: ಮೂಲಭೂತ ಪರಿಕರ್ಮಗಳು"><span>ಬದಲಾಯಿಸಿ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i><b>I</b></i> ಎಂಬುದು ಅನುಕ್ರಮಣಿಕೆ (ಇಂಡೆಕ್ಸ್ಡ್) ಇರುವ ಗಣವಾಗಿರಲಿ. <i><b>{Ai}<sub>iEI</sub></b></i> ಗಣಗಳ ಒಂದು ವ್ಯೂಹವಾಗಿರಲಿ (array of sets). <i><b>x</b></i> ಎಂಬುದು ಯಾವುದಾದರೂ ಒಂದು ಗಣ <i><b>A<sub>i</sub></b></i> ಗಾದರೂ ಧಾತುವಾಗಿದ್ದರೆ ಇಂಥ ಧಾತುಗಳ ಗಣಕ್ಕೆ <i><b>{Ai}<sub>iEI</sub></b></i> ಗಣಗಳ ಸಂಯೋಗ (<a href="https://en.wikipedia.org/wiki/Union_(set_theory)" class="extiw" title="en:Union (set theory)">ಯೂನಿಯನ್</a>) ಎಂದು ಹೆಸರು. ಇದನ್ನು <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 \bigcup _{I\in i}A_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>⋃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mo>∈</mo> <mi>i</mi> </mrow> </munder> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigcup _{I\in i}A_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6684495bf7bc9240faac03d7c050a35888bdb9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:5.511ex; height:5.676ex;" alt="{\displaystyle \bigcup _{I\in i}A_{i}}"></span>ಎಂದು ಬರೆಯುತ್ತೇವೆ. ε ಎಂಬುದು ಪ್ರತಿಯೊಂದು <i><b>A<sub>i</sub></b></i> ಗಣದ ಧಾತುವಾಗಿದ್ದರೆ ಇಂಥ ಧಾತುಗಳ ಗಣಕ್ಕೆ <i><b>{Ai}<sub>iEI</sub></b></i> ಗಣಗಳ ಛೇದನ (<a href="https://en.wikipedia.org/wiki/Intersection_(set_theory)" class="extiw" title="en:Intersection (set theory)">ಇಂಟರ್ಸೆಕ್ಷನ್</a>) ಎಂದು ಹೆಸರು. ಇದನ್ನು <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 \bigcap _{i\epsilon I}A_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>⋂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>ϵ</mi> <mi>I</mi> </mrow> </munder> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigcap _{i\epsilon I}A_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac9c896a77de5097003dea425a0affce673ab16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:5.511ex; height:5.509ex;" alt="{\displaystyle \bigcap _{i\epsilon I}A_{i}}"></span> ಎಂದು ಬರೆಯುತ್ತೇವೆ. <i><b>I</b></i> ಧನಪೂರ್ಣಾಂಕಗಳ (positive integer) ಗಣವಾಗಿದ್ದರೆ <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 \bigcup _{I\in i}A_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>⋃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mo>∈</mo> <mi>i</mi> </mrow> </munder> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigcup _{I\in i}A_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6684495bf7bc9240faac03d7c050a35888bdb9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:5.511ex; height:5.676ex;" alt="{\displaystyle \bigcup _{I\in i}A_{i}}"></span> ಮತ್ತು <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 \bigcap _{i\epsilon I}A_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>⋂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>ϵ</mi> <mi>I</mi> </mrow> </munder> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigcap _{i\epsilon I}A_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac9c896a77de5097003dea425a0affce673ab16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:5.511ex; height:5.509ex;" alt="{\displaystyle \bigcap _{i\epsilon I}A_{i}}"></span> ಎಣಿಕೆಮಾಡಬಲ್ಲ (ಕೌಂಟೆಬಲ್) ಸಂಯೋಗ ಛೇದಗಳಾಗುತ್ತವೆ. ಧಾತುವೇ ಇಲ್ಲದ ಗಣಕ್ಕೆ <a href="https://en.wikipedia.org/wiki/Empty_set" class="extiw" title="en:Empty set">ಶೂನ್ಯಗಣ</a> ಎಂದು ಹೆಸರು. ಉದಾಹರಣೆಗೆ <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 \chi \neq \chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>≠</mo> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi \neq \chi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33e347555744e3c5f49a80aaec13840442c735c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.009ex; height:2.676ex;" alt="{\displaystyle \chi \neq \chi }"></span>  ಆಗಿರುವಂಥ ವಾಸ್ತವ ಸಂಖ್ಯೆ <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 \chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.455ex; height:2.009ex;" alt="{\displaystyle \chi }"></span> ಗಳ ಗಣ ಶೂನ್ಯ ಗಣ. ಶೂನ್ಯಗಣವನ್ನು <i><b>∅</b></i> ಎಂದು ಬರೆಯುತ್ತೇವೆ. <i><b>A ∩ B = ∅</b></i> ಆದಾಗ ಮಾತ್ರ <i><b>A, B</b></i> ಗಣಗಳನ್ನು ಅಚ್ಛೇದ್ಯ (ಡಿಸ್ಜಾಯಿಂಟ್) ಎನ್ನುತ್ತೇವೆ. </p> <div class="mw-heading mw-heading2"><h2 id="ಉಲ್ಲೇಖಗಳು"><span id=".E0.B2.89.E0.B2.B2.E0.B3.8D.E0.B2.B2.E0.B3.87.E0.B2.96.E0.B2.97.E0.B2.B3.E0.B3.81"></span>ಉಲ್ಲೇಖಗಳು</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B2%97%E0%B2%A3_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4)&action=edit&section=5" title="ವಿಭಾಗ ಸಂಪಾದಿಸಿ: ಉಲ್ಲೇಖಗಳು"><span>ಬದಲಾಯಿಸಿ</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1256053">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.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-JainAhmad1995-1"><span class="mw-cite-backlink"><a href="#cite_ref-JainAhmad1995_1-0">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1256853">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFP._K._JainKhalil_AhmadOm_P._Ahuja1995" class="citation book cs1">P. K. Jain; Khalil Ahmad; Om P. Ahuja (1995). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=yZ68h97pnAkC&pg=PA1"><i>Functional Analysis</i></a>. New Age International. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/978-81-224-0801-0" title="ವಿಶೇಷ:BookSources/978-81-224-0801-0"><bdi>978-81-224-0801-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Functional+Analysis&rft.pages=1&rft.pub=New+Age+International&rft.date=1995&rft.isbn=978-81-224-0801-0&rft.au=P.+K.+Jain&rft.au=Khalil+Ahmad&rft.au=Om+P.+Ahuja&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DyZ68h97pnAkC%26pg%3DPA1&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-Goldberg1986-2"><span class="mw-cite-backlink"><a href="#cite_ref-Goldberg1986_2-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFSamuel_Goldberg1986" class="citation book cs1">Samuel Goldberg (1 January 1986). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=CmzFx9rB_FcC&pg=PA2"><i>Probability: An Introduction</i></a>. Courier Corporation. p. 2. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/978-0-486-65252-8" title="ವಿಶೇಷ:BookSources/978-0-486-65252-8"><bdi>978-0-486-65252-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Probability%3A+An+Introduction&rft.pages=2&rft.pub=Courier+Corporation&rft.date=1986-01-01&rft.isbn=978-0-486-65252-8&rft.au=Samuel+Goldberg&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DCmzFx9rB_FcC%26pg%3DPA2&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-CormenCormen2001-3"><span class="mw-cite-backlink"><a href="#cite_ref-CormenCormen2001_3-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFThomas_H._CormenCharles_E_LeisersonRonald_L_RivestClifford_Stein2001" class="citation book cs1">Thomas H. Cormen; Charles E Leiserson; Ronald L Rivest; Clifford Stein (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NLngYyWFl_YC&pg=PA1070"><i>Introduction To Algorithms</i></a>. MIT Press. p. 1070. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/978-0-262-03293-3" title="ವಿಶೇಷ:BookSources/978-0-262-03293-3"><bdi>978-0-262-03293-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+To+Algorithms&rft.pages=1070&rft.pub=MIT+Press&rft.date=2001&rft.isbn=978-0-262-03293-3&rft.au=Thomas+H.+Cormen&rft.au=Charles+E+Leiserson&rft.au=Ronald+L+Rivest&rft.au=Clifford+Stein&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DNLngYyWFl_YC%26pg%3DPA1070&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-MaurerRalston2005-4"><span class="mw-cite-backlink"><a href="#cite_ref-MaurerRalston2005_4-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFStephen_B._MaurerAnthony_Ralston2005" class="citation book cs1">Stephen B. Maurer; Anthony Ralston (21 January 2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=_0vNBQAAQBAJ&pg=PA11"><i>Discrete Algorithmic Mathematics</i></a>. CRC Press. p. 11. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/978-1-4398-6375-6" title="ವಿಶೇಷ:BookSources/978-1-4398-6375-6"><bdi>978-1-4398-6375-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discrete+Algorithmic+Mathematics&rft.pages=11&rft.pub=CRC+Press&rft.date=2005-01-21&rft.isbn=978-1-4398-6375-6&rft.au=Stephen+B.+Maurer&rft.au=Anthony+Ralston&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D_0vNBQAAQBAJ%26pg%3DPA11&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-:1-5"><span class="mw-cite-backlink"><a href="#cite_ref-:1_5-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mathsisfun.com/sets/sets-introduction.html">"Introduction to Sets"</a>. <i>www.mathsisfun.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-08-19</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.mathsisfun.com&rft.atitle=Introduction+to+Sets&rft_id=https%3A%2F%2Fwww.mathsisfun.com%2Fsets%2Fsets-introduction.html&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-DalenDoets2014-6"><span class="mw-cite-backlink"><a href="#cite_ref-DalenDoets2014_6-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFD._Van_DalenH._C._DoetsH._De_Swart2014" class="citation book cs1">D. Van Dalen; H. C. Doets; H. De Swart (9 May 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PfbiBQAAQBAJ&pg=PA1"><i>Sets: Naïve, Axiomatic and Applied: A Basic Compendium with Exercises for Use in Set Theory for Non Logicians, Working and Teaching Mathematicians and Students</i></a>. Elsevier Science. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/978-1-4831-5039-0" title="ವಿಶೇಷ:BookSources/978-1-4831-5039-0"><bdi>978-1-4831-5039-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sets%3A+Na%C3%AFve%2C+Axiomatic+and+Applied%3A+A+Basic+Compendium+with+Exercises+for+Use+in+Set+Theory+for+Non+Logicians%2C+Working+and+Teaching+Mathematicians+and+Students&rft.pages=1&rft.pub=Elsevier+Science&rft.date=2014-05-09&rft.isbn=978-1-4831-5039-0&rft.au=D.+Van+Dalen&rft.au=H.+C.+Doets&rft.au=H.+De+Swart&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPfbiBQAAQBAJ%26pg%3DPA1&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-Moschovakis1994-7"><span class="mw-cite-backlink"><a href="#cite_ref-Moschovakis1994_7-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFYiannis_N._Moschovakis1994" class="citation book cs1">Yiannis N. Moschovakis (1994). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ndx0_6VCypcC"><i>Notes on Set Theory</i></a>. Springer Science & Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/978-3-540-94180-4" title="ವಿಶೇಷ:BookSources/978-3-540-94180-4"><bdi>978-3-540-94180-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Notes+on+Set+Theory&rft.pub=Springer+Science+%26+Business+Media&rft.date=1994&rft.isbn=978-3-540-94180-4&rft.au=Yiannis+N.+Moschovakis&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dndx0_6VCypcC&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-Cantor.1891-8"><span class="mw-cite-backlink"><a href="#cite_ref-Cantor.1891_8-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFGeorg_Cantor1891" class="citation journal cs1">Georg Cantor (1891). <a rel="nofollow" class="external text" href="https://www.digizeitschriften.de/dms/img/?PID=GDZPPN002113910&physid=phys84#navi">"Ueber eine elementare Frage der Mannigfaltigkeitslehre"</a>. <i><a href="/w/index.php?title=Jahresbericht_der_Deutschen_Mathematiker-Vereinigung&action=edit&redlink=1" class="new" title="Jahresbericht der Deutschen Mathematiker-Vereinigung (ಪುಟವು ಇನ್ನೂ ಸೃಷ್ಟಿತವಾಗಿಲ್ಲ)">Jahresbericht der Deutschen Mathematiker-Vereinigung</a></i>. <b>1</b>: 75–78.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Jahresbericht+der+Deutschen+Mathematiker-Vereinigung&rft.atitle=Ueber+eine+elementare+Frage+der+Mannigfaltigkeitslehre&rft.volume=1&rft.pages=75-78&rft.date=1891&rft.au=Georg+Cantor&rft_id=https%3A%2F%2Fwww.digizeitschriften.de%2Fdms%2Fimg%2F%3FPID%3DGDZPPN002113910%26physid%3Dphys84%23navi&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span> English translation: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFEwald1996" class="citation book cs1">Ewald, William B., ed. (1996). <i>From Immanuel Kant to David Hilbert: A Source Book in the Foundations of Mathematics, Volume 2</i>. Oxford University Press. pp. 920–922. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/0-19-850536-1" title="ವಿಶೇಷ:BookSources/0-19-850536-1"><bdi>0-19-850536-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=From+Immanuel+Kant+to+David+Hilbert%3A+A+Source+Book+in+the+Foundations+of+Mathematics%2C+Volume+2&rft.pages=920-922&rft.pub=Oxford+University+Press&rft.date=1996&rft.isbn=0-19-850536-1&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-Hausdorff2005-9"><span class="mw-cite-backlink"><a href="#cite_ref-Hausdorff2005_9-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFFelix_Hausdorff2005" class="citation book cs1">Felix Hausdorff (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=yvVIdH16k0YC&pg=PA30"><i>Set Theory</i></a>. American Mathematical Soc. p. 30. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/978-0-8218-3835-8" title="ವಿಶೇಷ:BookSources/978-0-8218-3835-8"><bdi>978-0-8218-3835-8</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&rft.pages=30&rft.pub=American+Mathematical+Soc.&rft.date=2005&rft.isbn=978-0-8218-3835-8&rft.au=Felix+Hausdorff&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DyvVIdH16k0YC%26pg%3DPA30&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> <li id="cite_note-Lucas1990-10"><span class="mw-cite-backlink"><a href="#cite_ref-Lucas1990_10-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256853"><cite id="CITEREFJohn_F._Lucas1990" class="citation book cs1">John F. Lucas (1990). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=jklsb5JUgoQC&pg=PA108"><i>Introduction to Abstract Mathematics</i></a>. Rowman & Littlefield. p. 108. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%87%E0%B2%B7:BookSources/978-0-912675-73-2" title="ವಿಶೇಷ:BookSources/978-0-912675-73-2"><bdi>978-0-912675-73-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Abstract+Mathematics&rft.pages=108&rft.pub=Rowman+%26+Littlefield&rft.date=1990&rft.isbn=978-0-912675-73-2&rft.au=John+F.+Lucas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Djklsb5JUgoQC%26pg%3DPA108&rfr_id=info%3Asid%2Fkn.wikipedia.org%3A%E0%B2%97%E0%B2%A3+%28%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%29" class="Z3988"></span></span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div 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