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[r]" accesskey="r"><span>Апошнія зьмены</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%9D%D0%BE%D0%B2%D1%8B%D1%8F_%D1%81%D1%82%D0%B0%D1%80%D0%BE%D0%BD%D0%BA%D1%96"><span>Новыя старонкі</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D1%8D%D0%B4%D1%8B%D1%8F:%D0%94%D0%B0%D0%BF%D0%B0%D0%BC%D0%BE%D0%B3%D0%B0" title="Месца, каб пра ўсё даведацца"><span>Дапамога</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/%D0%93%D0%B0%D0%BB%D0%BE%D1%9E%D0%BD%D0%B0%D1%8F_%D1%81%D1%82%D0%B0%D1%80%D0%BE%D0%BD%D0%BA%D0%B0" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Вікіпэдыя" src="/static/images/mobile/copyright/wikipedia-wordmark-be_x_old.svg" style="width: 7.5em; height: 1.3125em;"> <img class="mw-logo-tagline" alt="вольная энцыкляпэдыя" src="/static/images/mobile/copyright/wikipedia-tagline-be_x_old.svg" width="120" height="12" style="width: 7.5em; height: 0.75em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%9F%D0%BE%D1%88%D1%83%D0%BA" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Шукаць у Вікіпэдыі [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Пошук</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Пошук у Вікіпэдыі" aria-label="Пошук у Вікіпэдыі" autocapitalize="sentences" title="Шукаць у Вікіпэдыі [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Спэцыяльныя:Пошук"> </div> <button class="cdx-button cdx-search-input__end-button">Пошук</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Асабістыя прылады"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Выгляд"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Выгляд" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Выгляд</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_be-x-old.wikipedia.org&uselang=be-tarask" class=""><span>Ахвяраваньні</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%A1%D1%82%D0%B2%D0%B0%D1%80%D1%8B%D1%86%D1%8C_%D1%80%D0%B0%D1%85%D1%83%D0%BD%D0%B0%D0%BA&returnto=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B+%D0%BB%D1%96%D0%BA" title="Мы прапануем вам стварыць уліковы запіс і ўвайсьці, але гэта не абавязкова" class=""><span>Стварыць уліковы запіс</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%A3%D0%B2%D0%B0%D1%85%D0%BE%D0%B4_%D1%83_%D1%81%D1%8B%D1%81%D1%82%D1%8D%D0%BC%D1%83&returnto=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B+%D0%BB%D1%96%D0%BA" title="Вас запрашаюць увайсьці, хаця гэта і неабавязкова. [o]" accesskey="o" class=""><span>Увайсьці</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="Болей парамэтраў" > <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="Асабістыя прылады" > <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">Асабістыя прылады</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Карыстацкае мэню" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_be-x-old.wikipedia.org&uselang=be-tarask"><span>Ахвяраваньні</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%A1%D1%82%D0%B2%D0%B0%D1%80%D1%8B%D1%86%D1%8C_%D1%80%D0%B0%D1%85%D1%83%D0%BD%D0%B0%D0%BA&returnto=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B+%D0%BB%D1%96%D0%BA" title="Мы прапануем вам стварыць уліковы запіс і ўвайсьці, але гэта не абавязкова"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Стварыць уліковы запіс</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%A3%D0%B2%D0%B0%D1%85%D0%BE%D0%B4_%D1%83_%D1%81%D1%8B%D1%81%D1%82%D1%8D%D0%BC%D1%83&returnto=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B+%D0%BB%D1%96%D0%BA" title="Вас запрашаюць увайсьці, хаця гэта і неабавязкова. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Увайсьці</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"> Старонкі для неаўтарызаваных рэдактараў <a href="/wiki/%D0%94%D0%B0%D0%BF%D0%B0%D0%BC%D0%BE%D0%B3%D0%B0:%D0%A3%D0%B2%D0%BE%D0%B4%D0%B7%D1%96%D0%BD%D1%8B" aria-label="Даведайцеся пра рэдагаваньне болей"><span>даведацца болей</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/%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%9C%D0%BE%D0%B9_%D1%83%D0%BD%D1%91%D1%81%D0%B0%D0%BA" title="Сьпіс рэдагаваньняў, зробленых з гэтага IP-адрасу [y]" accesskey="y"><span>Унёсак</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%9C%D0%B0%D0%B5_%D1%80%D0%B0%D0%B7%D0%BC%D0%BE%D0%B2%D1%8B" title="Старонка гутарак пра рэдагаваньні, зробленыя з гэтага IP-адрасу [n]" accesskey="n"><span>Гутаркі</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Сайт"> <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="Зьмест" 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">Зьмест</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">перанесьці ў бакавую панэль</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">схаваць</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">Пачатак</div> </a> </li> <li id="toc-Гісторыя" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Гісторыя"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Гісторыя</span> </div> </a> <ul id="toc-Гісторыя-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Аксіёматычнае_ўвядзеньне_Пэана" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Аксіёматычнае_ўвядзеньне_Пэана"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Аксіёматычнае ўвядзеньне Пэана</span> </div> </a> <ul id="toc-Аксіёматычнае_ўвядзеньне_Пэана-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Тэарэтыка-мноственнае_ўвядзеньне" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Тэарэтыка-мноственнае_ўвядзеньне"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Тэарэтыка-мноственнае ўвядзеньне</span> </div> </a> <ul id="toc-Тэарэтыка-мноственнае_ўвядзеньне-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Уласьцівасьці" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Уласьцівасьці"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Уласьцівасьці</span> </div> </a> <ul id="toc-Уласьцівасьці-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Літаратура" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Літаратура"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Літаратура</span> </div> </a> <ul id="toc-Літаратура-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="Зьмест" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Схаваць/паказаць зьмест" > <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">Схаваць/паказаць зьмест</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">Натуральны лік</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="Перайсьці да артыкула на іншай мове. Выбраць з: 148 languages" > <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-148" 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">148 моваў</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Natuurlike_getal" title="Natuurlike getal — афрыкаанс" lang="af" hreflang="af" data-title="Natuurlike getal" data-language-autonym="Afrikaans" data-language-local-name="афрыкаанс" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Nat%C3%BCrliche_Zahl" title="Natürliche Zahl — швайцарская нямецкая" lang="gsw" hreflang="gsw" data-title="Natürliche Zahl" data-language-autonym="Alemannisch" data-language-local-name="швайцарская нямецкая" 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%8B%A8%E1%89%B0%E1%8D%88%E1%8C%A5%E1%88%AE_%E1%89%81%E1%8C%A5%E1%88%AD" title="የተፈጥሮ ቁጥር — амгарская" lang="am" hreflang="am" data-title="የተፈጥሮ ቁጥር" data-language-autonym="አማርኛ" data-language-local-name="амгарская" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A4%BF%E0%A4%95_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="प्राकृतिक संख्या — ангіцкая" lang="anp" hreflang="anp" data-title="प्राकृतिक संख्या" data-language-autonym="अंगिका" data-language-local-name="ангіцкая" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ab mw-list-item"><a href="https://ab.wikipedia.org/wiki/%D0%98%D4%A5%D1%81%D0%B0%D0%B1%D0%B0%D1%80%D0%B0%D1%82%D3%99%D1%83_%D0%B0%D1%85%D1%8B%D4%A5%D1%85%D1%8C%D0%B0%D3%A1%D0%B0%D1%80%D0%B0" title="Иԥсабаратәу ахыԥхьаӡара — абхаская" lang="ab" hreflang="ab" data-title="Иԥсабаратәу ахыԥхьаӡара" data-language-autonym="Аԥсшәа" data-language-local-name="абхаская" class="interlanguage-link-target"><span>Аԥсшәа</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%B7%D8%A8%D9%8A%D8%B9%D9%8A" title="عدد طبيعي — арабская" lang="ar" hreflang="ar" data-title="عدد طبيعي" data-language-autonym="العربية" data-language-local-name="арабская" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Numero_natural" title="Numero natural — арагонская" lang="an" hreflang="an" data-title="Numero natural" data-language-autonym="Aragonés" data-language-local-name="арагонская" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B2%D5%B6%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A9%D5%AB%D6%82" title="Բնական թիւ — Western Armenian" lang="hyw" hreflang="hyw" data-title="Բնական թիւ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B8%E0%A7%8D%E0%A6%AC%E0%A6%BE%E0%A6%AD%E0%A6%BE%E0%A7%B1%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="স্বাভাৱিক সংখ্যা — асамская" lang="as" hreflang="as" data-title="স্বাভাৱিক সংখ্যা" data-language-autonym="অসমীয়া" data-language-local-name="асамская" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/N%C3%BAmberu_natural" title="Númberu natural — астурыйская" lang="ast" hreflang="ast" data-title="Númberu natural" data-language-autonym="Asturianu" data-language-local-name="астурыйская" 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/Natural_%C9%99d%C9%99dl%C9%99r" title="Natural ədədlər — азэрбайджанская" lang="az" hreflang="az" data-title="Natural ədədlər" data-language-autonym="Azərbaycanca" data-language-local-name="азэрбайджанская" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B7%D8%A8%DB%8C%D8%B9%DB%8C_%D8%B3%D8%A7%DB%8C%DB%8C%D9%84%D8%A7%D8%B1" title="طبیعی ساییلار — South Azerbaijani" lang="azb" hreflang="azb" data-title="طبیعی ساییلار" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%8D%E0%A6%AC%E0%A6%BE%E0%A6%AD%E0%A6%BE%E0%A6%AC%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="স্বাভাবিক সংখ্যা — бэнгальская" lang="bn" hreflang="bn" data-title="স্বাভাবিক সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="бэнгальская" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ch%C5%AB-ji%C3%A2n-s%C3%B2%CD%98" title="Chū-jiân-sò͘ — Minnan" lang="nan" hreflang="nan" data-title="Chū-jiân-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C_%D2%BB%D0%B0%D0%BD" title="Натураль һан — башкірская" lang="ba" hreflang="ba" data-title="Натураль һан" data-language-autonym="Башҡортса" data-language-local-name="башкірская" 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%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Натуральны лік — беларуская" lang="be" hreflang="be" data-title="Натуральны лік" data-language-autonym="Беларуская" data-language-local-name="беларуская" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D1%81%D1%82%D0%B5%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Естествено число — баўгарская" lang="bg" hreflang="bg" data-title="Естествено число" data-language-autonym="Български" data-language-local-name="баўгарская" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A2%E0%BD%84%E0%BC%8B%E0%BD%96%E0%BE%B1%E0%BD%B4%E0%BD%84%E0%BC%8B%E0%BD%82%E0%BE%B2%E0%BD%84%E0%BD%A6%E0%BC%8D" title="རང་བྱུང་གྲངས། — тыбэцкая" lang="bo" hreflang="bo" data-title="རང་བྱུང་གྲངས།" data-language-autonym="བོད་ཡིག" data-language-local-name="тыбэцкая" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Prirodan_broj" title="Prirodan broj — басьнійская" lang="bs" hreflang="bs" data-title="Prirodan broj" data-language-autonym="Bosanski" data-language-local-name="басьнійская" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Niver_naturel" title="Niver naturel — брэтонская" lang="br" hreflang="br" data-title="Niver naturel" data-language-autonym="Brezhoneg" data-language-local-name="брэтонская" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_natural" title="Nombre natural — каталёнская" lang="ca" hreflang="ca" data-title="Nombre natural" data-language-autonym="Català" data-language-local-name="каталёнская" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D1%83%D1%80%D0%BB%C4%83%D1%85_%D1%85%D0%B8%D1%81%D0%B5%D0%BF%C4%95" title="Пурлăх хисепĕ — чуваская" lang="cv" hreflang="cv" data-title="Пурлăх хисепĕ" data-language-autonym="Чӑвашла" data-language-local-name="чуваская" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/P%C5%99irozen%C3%A9_%C4%8D%C3%ADslo" title="Přirozené číslo — чэская" lang="cs" hreflang="cs" data-title="Přirozené číslo" data-language-autonym="Čeština" data-language-local-name="чэская" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhif_naturiol" title="Rhif naturiol — валійская" lang="cy" hreflang="cy" data-title="Rhif naturiol" data-language-autonym="Cymraeg" data-language-local-name="валійская" 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/Naturligt_tal" title="Naturligt tal — дацкая" lang="da" hreflang="da" data-title="Naturligt tal" data-language-autonym="Dansk" data-language-local-name="дацкая" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B9%D8%A7%D8%AF%D8%A7%D8%AF_%D8%B7%D8%A8%D9%8A%D8%B9%D9%8A" title="عاداد طبيعي — Moroccan Arabic" lang="ary" hreflang="ary" data-title="عاداد طبيعي" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Nat%C3%BCrliche_Zahl" title="Natürliche Zahl — нямецкая" lang="de" hreflang="de" data-title="Natürliche Zahl" data-language-autonym="Deutsch" data-language-local-name="нямецкая" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Naturaalarv" title="Naturaalarv — эстонская" lang="et" hreflang="et" data-title="Naturaalarv" data-language-autonym="Eesti" data-language-local-name="эстонская" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A6%CF%85%CF%83%CE%B9%CE%BA%CF%8C%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82" title="Φυσικός αριθμός — грэцкая" lang="el" hreflang="el" data-title="Φυσικός αριθμός" data-language-autonym="Ελληνικά" data-language-local-name="грэцкая" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/N%C3%B3mmer_natur%C3%A8l" title="Nómmer naturèl — Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Nómmer naturèl" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Natural_number" title="Natural number — ангельская" lang="en" hreflang="en" data-title="Natural number" data-language-autonym="English" data-language-local-name="ангельская" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_natural" title="Número natural — гішпанская" lang="es" hreflang="es" data-title="Número natural" data-language-autonym="Español" data-language-local-name="гішпанская" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Natura_nombro" title="Natura nombro — эспэранта" lang="eo" hreflang="eo" data-title="Natura nombro" data-language-autonym="Esperanto" data-language-local-name="эспэранта" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki_arrunt" title="Zenbaki arrunt — баскаўская" lang="eu" hreflang="eu" data-title="Zenbaki arrunt" data-language-autonym="Euskara" data-language-local-name="баскаўская" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%B7%D8%A8%DB%8C%D8%B9%DB%8C" title="عدد طبیعی — пэрсыдзкая" lang="fa" hreflang="fa" data-title="عدد طبیعی" data-language-autonym="فارسی" data-language-local-name="пэрсыдзкая" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Teljital" title="Teljital — фарэрская" lang="fo" hreflang="fo" data-title="Teljital" data-language-autonym="Føroyskt" data-language-local-name="фарэрская" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Entier_naturel" title="Entier naturel — француская" lang="fr" hreflang="fr" data-title="Entier naturel" data-language-autonym="Français" data-language-local-name="француская" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Uimhir_aiceanta" title="Uimhir aiceanta — ірляндзкая" lang="ga" hreflang="ga" data-title="Uimhir aiceanta" data-language-autonym="Gaeilge" data-language-local-name="ірляндзкая" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%BAmero_natural" title="Número natural — галіцыйская" lang="gl" hreflang="gl" data-title="Número natural" data-language-autonym="Galego" data-language-local-name="галіцыйская" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%91%D0%BE%D0%BA%D1%8A%D0%BE%D0%BD%D1%86%D0%B0_%D0%B4%D0%BE%D0%BB%D0%B0_%D1%82%D0%B0%D1%8C%D1%80%D0%B0%D1%85%D1%8C" title="Бокъонца дола таьрахь — інгуская" lang="inh" hreflang="inh" data-title="Бокъонца дола таьрахь" data-language-autonym="ГӀалгӀай" data-language-local-name="інгуская" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E6%95%B8" title="自然數 — Gan" lang="gan" hreflang="gan" data-title="自然數" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AA%E0%AB%8D%E0%AA%B0%E0%AA%BE%E0%AA%95%E0%AB%83%E0%AA%A4%E0%AA%BF%E0%AA%95_%E0%AA%B8%E0%AA%82%E0%AA%96%E0%AB%8D%E0%AA%AF%E0%AA%BE%E0%AA%93" title="પ્રાકૃતિક સંખ્યાઓ — гуджарацкая" lang="gu" hreflang="gu" data-title="પ્રાકૃતિક સંખ્યાઓ" data-language-autonym="ગુજરાતી" data-language-local-name="гуджарацкая" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%99%D0%B8%D1%80%D1%82%D0%B8%D0%BC%D2%97%D0%B8%D0%BD_%D1%82%D0%BE%D0%B9%D0%B3" title="Йиртимҗин тойг — калмыцкая" lang="xal" hreflang="xal" data-title="Йиртимҗин тойг" data-language-autonym="Хальмг" data-language-local-name="калмыцкая" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9E%90%EC%97%B0%EC%88%98" title="자연수 — карэйская" lang="ko" hreflang="ko" data-title="자연수" data-language-autonym="한국어" data-language-local-name="карэйская" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%B6%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A9%D5%AB%D5%BE" title="Բնական թիվ — армянская" lang="hy" hreflang="hy" data-title="Բնական թիվ" data-language-autonym="Հայերեն" data-language-local-name="армянская" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A4%BF%E0%A4%95_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="प्राकृतिक संख्या — гіндзі" lang="hi" hreflang="hi" data-title="प्राकृतिक संख्या" data-language-autonym="हिन्दी" data-language-local-name="гіндзі" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/P%C5%99irodna_li%C4%8Dba" title="Přirodna ličba — верхнялужыцкая" lang="hsb" hreflang="hsb" data-title="Přirodna ličba" data-language-autonym="Hornjoserbsce" data-language-local-name="верхнялужыцкая" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Prirodni_broj" title="Prirodni broj — харвацкая" lang="hr" hreflang="hr" data-title="Prirodni broj" data-language-autonym="Hrvatski" data-language-local-name="харвацкая" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Naturala_nombro" title="Naturala nombro — ідзкая" lang="io" hreflang="io" data-title="Naturala nombro" data-language-autonym="Ido" data-language-local-name="ідзкая" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan_asli" title="Bilangan asli — інданэзійская" lang="id" hreflang="id" data-title="Bilangan asli" data-language-autonym="Bahasa Indonesia" data-language-local-name="інданэзійская" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Numero_natural" title="Numero natural — інтэрлінгва" lang="ia" hreflang="ia" data-title="Numero natural" data-language-autonym="Interlingua" data-language-local-name="інтэрлінгва" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D0%BE%D0%BD_%D0%BD%D1%8B%D0%BC%C3%A6%D1%86" title="Натуралон нымæц — асэтынская" lang="os" hreflang="os" data-title="Натуралон нымæц" data-language-autonym="Ирон" data-language-local-name="асэтынская" class="interlanguage-link-target"><span>Ирон</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/Amanani_a-natural" title="Amanani a-natural — коская" lang="xh" hreflang="xh" data-title="Amanani a-natural" data-language-autonym="IsiXhosa" data-language-local-name="коская" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Inombolo_Yokubala" title="Inombolo Yokubala — зулуская" lang="zu" hreflang="zu" data-title="Inombolo Yokubala" data-language-autonym="IsiZulu" data-language-local-name="зулуская" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/N%C3%A1tt%C3%BArlegar_t%C3%B6lur" title="Náttúrlegar tölur — ісьляндзкая" lang="is" hreflang="is" data-title="Náttúrlegar tölur" data-language-autonym="Íslenska" data-language-local-name="ісьляндзкая" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_naturale" title="Numero naturale — італьянская" lang="it" hreflang="it" data-title="Numero naturale" data-language-autonym="Italiano" data-language-local-name="італьянская" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%98%D7%91%D7%A2%D7%99" title="מספר טבעי — іўрыт" lang="he" hreflang="he" data-title="מספר טבעי" data-language-autonym="עברית" data-language-local-name="іўрыт" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Wilangan_asli" title="Wilangan asli — яванская" lang="jv" hreflang="jv" data-title="Wilangan asli" data-language-autonym="Jawa" data-language-local-name="яванская" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Pilim_%C3%B1%CA%8A%CA%8A" title="Pilim ñʊʊ — Kabiye" lang="kbp" hreflang="kbp" data-title="Pilim ñʊʊ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/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 — канадзкая" lang="kn" hreflang="kn" data-title="ಸ್ವಾಭಾವಿಕ ಸಂಖ್ಯೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="канадзкая" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9C%E1%83%90%E1%83%A2%E1%83%A3%E1%83%A0%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%98" title="ნატურალური რიცხვი — грузінская" lang="ka" hreflang="ka" data-title="ნატურალური რიცხვი" data-language-autonym="ქართული" data-language-local-name="грузінская" 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%94%D0%B0%D2%93%D0%B4%D1%8B%D0%BB%D1%8B_%D1%81%D0%B0%D0%BD" title="Дағдылы сан — казаская" lang="kk" hreflang="kk" data-title="Дағдылы сан" data-language-autonym="Қазақша" data-language-local-name="казаская" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Namba_asilia" title="Namba asilia — суахілі" lang="sw" hreflang="sw" data-title="Namba asilia" data-language-autonym="Kiswahili" data-language-local-name="суахілі" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Anty%C3%A9_natir%C3%A8l" title="Antyé natirèl — Guianan Creole" lang="gcr" hreflang="gcr" data-title="Antyé natirèl" 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-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Hejmar%C3%AAn_xwezay%C3%AE" title="Hejmarên xwezayî — курдзкая" lang="ku" hreflang="ku" data-title="Hejmarên xwezayî" data-language-autonym="Kurdî" data-language-local-name="курдзкая" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D0%B4%D1%8B%D0%BA_%D1%81%D0%B0%D0%BD" title="Натуралдык сан — кыргыская" lang="ky" hreflang="ky" data-title="Натуралдык сан" data-language-autonym="Кыргызча" data-language-local-name="кыргыская" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%88%E0%BA%B3%E0%BA%99%E0%BA%A7%E0%BA%99%E0%BA%97%E0%BA%B3%E0%BA%A1%E0%BA%B0%E0%BA%8A%E0%BA%B2%E0%BA%94" title="ຈຳນວນທຳມະຊາດ — лаоская" lang="lo" hreflang="lo" data-title="ຈຳນວນທຳມະຊາດ" data-language-autonym="ລາວ" data-language-local-name="лаоская" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numerus_naturalis" title="Numerus naturalis — лацінская" lang="la" hreflang="la" data-title="Numerus naturalis" data-language-autonym="Latina" data-language-local-name="лацінская" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Natur%C4%81ls_skaitlis" title="Naturāls skaitlis — латыская" lang="lv" hreflang="lv" data-title="Naturāls skaitlis" data-language-autonym="Latviešu" data-language-local-name="латыская" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Natierlech_Zuel" title="Natierlech Zuel — люксэмбурская" lang="lb" hreflang="lb" data-title="Natierlech Zuel" data-language-autonym="Lëtzebuergesch" data-language-local-name="люксэмбурская" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Nat%C5%ABralusis_skai%C4%8Dius" title="Natūralusis skaičius — летувіская" lang="lt" hreflang="lt" data-title="Natūralusis skaičius" data-language-autonym="Lietuvių" data-language-local-name="летувіская" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Natuurlek_getal" title="Natuurlek getal — лімбурская" lang="li" hreflang="li" data-title="Natuurlek getal" data-language-autonym="Limburgs" data-language-local-name="лімбурская" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Numero_natural" title="Numero natural — Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Numero natural" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/kacna%27u" title="kacna'u — ложбанская" lang="jbo" hreflang="jbo" data-title="kacna'u" data-language-autonym="La .lojban." data-language-local-name="ложбанская" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/N%C3%BCmar_nat%C3%BCraal" title="Nümar natüraal — Lombard" lang="lmo" hreflang="lmo" data-title="Nümar natüraal" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Term%C3%A9szetes_sz%C3%A1mok" title="Természetes számok — вугорская" lang="hu" hreflang="hu" data-title="Természetes számok" data-language-autonym="Magyar" data-language-local-name="вугорская" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D1%80%D0%BE%D0%B4%D0%B5%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Природен број — македонская" lang="mk" hreflang="mk" data-title="Природен број" data-language-autonym="Македонски" data-language-local-name="македонская" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Isa_nanahary" title="Isa nanahary — малягасійская" lang="mg" hreflang="mg" data-title="Isa nanahary" data-language-autonym="Malagasy" data-language-local-name="малягасійская" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%8E%E0%B4%A3%E0%B5%8D%E0%B4%A3%E0%B5%BD_%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF" title="എണ്ണൽ സംഖ്യ — малаяламская" lang="ml" hreflang="ml" data-title="എണ്ണൽ സംഖ്യ" data-language-autonym="മലയാളം" data-language-local-name="малаяламская" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Numru_naturali" title="Numru naturali — мальтыйская" lang="mt" hreflang="mt" data-title="Numru naturali" data-language-autonym="Malti" data-language-local-name="мальтыйская" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A8%E0%A5%88%E0%A4%B8%E0%A4%B0%E0%A5%8D%E0%A4%97%E0%A4%BF%E0%A4%95_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="नैसर्गिक संख्या — маратгійская" lang="mr" hreflang="mr" data-title="नैसर्गिक संख्या" data-language-autonym="मराठी" data-language-local-name="маратгійская" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%B7%D8%A8%D9%8A%D8%B9%D9%89" title="عدد طبيعى — эгіпецкая арабская" lang="arz" hreflang="arz" data-title="عدد طبيعى" data-language-autonym="مصرى" data-language-local-name="эгіпецкая арабская" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Nombor_asli" title="Nombor asli — малайская" lang="ms" hreflang="ms" data-title="Nombor asli" data-language-autonym="Bahasa Melayu" data-language-local-name="малайская" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/N%C3%BAmaro_natural" title="Númaro natural — мірандыйская" lang="mwl" hreflang="mwl" data-title="Númaro natural" data-language-autonym="Mirandés" data-language-local-name="мірандыйская" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE" title="Натурал тоо — мангольская" lang="mn" hreflang="mn" data-title="Натурал тоо" data-language-autonym="Монгол" data-language-local-name="мангольская" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%98%E1%80%AC%E1%80%9D%E1%80%80%E1%80%AD%E1%80%94%E1%80%BA%E1%80%B8" title="သဘာဝကိန်း — бірманская" lang="my" hreflang="my" data-title="သဘာဝကိန်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="бірманская" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Naba_vakatamata" title="Naba vakatamata — фіджыйская" lang="fj" hreflang="fj" data-title="Naba vakatamata" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="фіджыйская" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Natuurlijk_getal" title="Natuurlijk getal — нідэрляндзкая" lang="nl" hreflang="nl" data-title="Natuurlijk getal" data-language-autonym="Nederlands" data-language-local-name="нідэрляндзкая" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A4%BF%E0%A4%95_%E0%A4%B8%E0%A4%99%E0%A5%8D%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="प्राकृतिक सङ्ख्या — нэпальская" lang="ne" hreflang="ne" data-title="प्राकृतिक सङ्ख्या" data-language-autonym="नेपाली" data-language-local-name="нэпальская" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A4%BF%E0%A4%95_%E0%A4%B2%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%83" title="प्राकृतिक ल्याः — неўарыйская" lang="new" hreflang="new" data-title="प्राकृतिक ल्याः" data-language-autonym="नेपाल भाषा" data-language-local-name="неўарыйская" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E6%95%B0" title="自然数 — японская" lang="ja" hreflang="ja" data-title="自然数" data-language-autonym="日本語" data-language-local-name="японская" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Nat%C3%BC%C3%BCrelk_taal" title="Natüürelk taal — паўночнафрызская" lang="frr" hreflang="frr" data-title="Natüürelk taal" data-language-autonym="Nordfriisk" data-language-local-name="паўночнафрызская" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Naturlig_tall" title="Naturlig tall — нарвэская (букмал)" lang="nb" hreflang="nb" data-title="Naturlig tall" data-language-autonym="Norsk bokmål" data-language-local-name="нарвэская (букмал)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Naturleg_tal" title="Naturleg tal — нарвэская (нюнашк)" lang="nn" hreflang="nn" data-title="Naturleg tal" data-language-autonym="Norsk nynorsk" data-language-local-name="нарвэская (нюнашк)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Enti%C3%A8r_natural" title="Entièr natural — аксытанская" lang="oc" hreflang="oc" data-title="Entièr natural" data-language-autonym="Occitan" data-language-local-name="аксытанская" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%97%E0%AC%A3%E0%AC%A8_%E0%AC%B8%E0%AC%82%E0%AC%96%E0%AD%8D%E0%AD%9F%E0%AC%BE" title="ଗଣନ ସଂଖ୍ୟା — орыянская" lang="or" hreflang="or" data-title="ଗଣନ ସଂଖ୍ୟା" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="орыянская" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Lakkoofsa_lakkaawwii" title="Lakkoofsa lakkaawwii — аромская" lang="om" hreflang="om" data-title="Lakkoofsa lakkaawwii" data-language-autonym="Oromoo" data-language-local-name="аромская" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Natural_son" title="Natural son — узбэцкая" lang="uz" hreflang="uz" data-title="Natural son" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбэцкая" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%81%E0%A8%A6%E0%A8%B0%E0%A8%A4%E0%A9%80_%E0%A8%85%E0%A9%B0%E0%A8%95" title="ਕੁਦਰਤੀ ਅੰਕ — панджабская" lang="pa" hreflang="pa" data-title="ਕੁਦਰਤੀ ਅੰਕ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="панджабская" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%86%DB%8C%DA%86%D8%B1%D9%84_%D9%86%D9%85%D8%A8%D8%B1" title="نیچرل نمبر — Western Punjabi" lang="pnb" hreflang="pnb" data-title="نیچرل نمبر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Nachral_nomba" title="Nachral nomba — Jamaican Creole English" lang="jam" hreflang="jam" data-title="Nachral nomba" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%85%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%93%E1%9E%82%E1%9E%8F%E1%9F%8B%E1%9E%92%E1%9E%98%E1%9F%92%E1%9E%98%E1%9E%87%E1%9E%B6%E1%9E%8F%E1%9E%B7" title="ចំនួនគត់ធម្មជាតិ — кгмэрская" lang="km" hreflang="km" data-title="ចំនួនគត់ធម្មជាតិ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="кгмэрская" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/N%C3%B9mer_natural" title="Nùmer natural — Piedmontese" lang="pms" hreflang="pms" data-title="Nùmer natural" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Nat%C3%BCrliche_Tall" title="Natürliche Tall — ніжненямецкая" lang="nds" hreflang="nds" data-title="Natürliche Tall" data-language-autonym="Plattdüütsch" data-language-local-name="ніжненямецкая" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczby_naturalne" title="Liczby naturalne — польская" lang="pl" hreflang="pl" data-title="Liczby naturalne" data-language-autonym="Polski" data-language-local-name="польская" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero_natural" title="Número natural — партугальская" lang="pt" hreflang="pt" data-title="Número natural" data-language-autonym="Português" data-language-local-name="партугальская" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ksh mw-list-item"><a href="https://ksh.wikipedia.org/wiki/Nat%C3%B6rliche_Zahle" title="Natörliche Zahle — кёльнская" lang="ksh" hreflang="ksh" data-title="Natörliche Zahle" data-language-autonym="Ripoarisch" data-language-local-name="кёльнская" class="interlanguage-link-target"><span>Ripoarisch</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_natural" title="Număr natural — румынская" lang="ro" hreflang="ro" data-title="Număr natural" data-language-autonym="Română" data-language-local-name="румынская" 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%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Натуральное число — расейская" lang="ru" hreflang="ru" data-title="Натуральное число" data-language-autonym="Русский" data-language-local-name="расейская" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D0%B9_%D1%87%D1%8B%D1%8Bh%D1%8B%D0%BB%D0%B0%D2%95%D0%B0" title="Натуральнай чыыhылаҕа — якуцкая" lang="sah" hreflang="sah" data-title="Натуральнай чыыhылаҕа" data-language-autonym="Саха тыла" data-language-local-name="якуцкая" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A4%B8%E0%A4%99%E0%A5%8D%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="प्राकृतिकसङ्ख्या — санскрыт" lang="sa" hreflang="sa" data-title="प्राकृतिकसङ्ख्या" data-language-autonym="संस्कृतम्" data-language-local-name="санскрыт" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/N%C3%B9meru_naturale" title="Nùmeru naturale — сардынская" lang="sc" hreflang="sc" data-title="Nùmeru naturale" data-language-autonym="Sardu" data-language-local-name="сардынская" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Numrat_natyror%C3%AB" title="Numrat natyrorë — альбанская" lang="sq" hreflang="sq" data-title="Numrat natyrorë" data-language-autonym="Shqip" data-language-local-name="альбанская" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/N%C3%B9mmuru_naturali" title="Nùmmuru naturali — сыцылійская" lang="scn" hreflang="scn" data-title="Nùmmuru naturali" data-language-autonym="Sicilianu" data-language-local-name="сыцылійская" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B7%8A%E0%B7%80%E0%B7%8F%E0%B6%B7%E0%B7%8F%E0%B7%80%E0%B7%92%E0%B6%9A_%E0%B7%83%E0%B6%82%E0%B6%9B%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F" title="ස්වාභාවික සංඛ්‍යා — сынгальская" lang="si" hreflang="si" data-title="ස්වාභාවික සංඛ්‍යා" data-language-autonym="සිංහල" data-language-local-name="сынгальская" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Natural_number" title="Natural number — спрошчаная ангельская" lang="en-simple" hreflang="en-simple" data-title="Natural number" data-language-autonym="Simple English" data-language-local-name="спрошчаная ангельская" 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/Prirodzen%C3%A9_%C4%8D%C3%ADslo" title="Prirodzené číslo — славацкая" lang="sk" hreflang="sk" data-title="Prirodzené číslo" data-language-autonym="Slovenčina" data-language-local-name="славацкая" 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/Naravno_%C5%A1tevilo" title="Naravno število — славенская" lang="sl" hreflang="sl" data-title="Naravno število" data-language-autonym="Slovenščina" data-language-local-name="славенская" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Naturalno_n%C5%AFmera" title="Naturalno nůmera — Silesian" lang="szl" hreflang="szl" data-title="Naturalno nůmera" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Thiin_tirsiimo" title="Thiin tirsiimo — самалійская" lang="so" hreflang="so" data-title="Thiin tirsiimo" data-language-autonym="Soomaaliga" data-language-local-name="самалійская" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95%DB%8C_%D8%B3%D8%B1%D9%88%D8%B4%D8%AA%DB%8C" title="ژمارەی سروشتی — цэнтральнакурдзкая" lang="ckb" hreflang="ckb" data-title="ژمارەی سروشتی" data-language-autonym="کوردی" data-language-local-name="цэнтральнакурдзкая" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D1%80%D0%BE%D0%B4%D0%B0%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Природан број — сэрбская" lang="sr" hreflang="sr" data-title="Природан број" data-language-autonym="Српски / srpski" data-language-local-name="сэрбская" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Prirodan_broj" title="Prirodan broj — сэрбскахарвацкая" lang="sh" hreflang="sh" data-title="Prirodan broj" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="сэрбскахарвацкая" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Luonnollinen_luku" title="Luonnollinen luku — фінская" lang="fi" hreflang="fi" data-title="Luonnollinen luku" data-language-autonym="Suomi" data-language-local-name="фінская" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Naturliga_tal" title="Naturliga tal — швэдзкая" lang="sv" hreflang="sv" data-title="Naturliga tal" data-language-autonym="Svenska" data-language-local-name="швэдзкая" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Likas_na_bilang" title="Likas na bilang — Tagalog" lang="tl" hreflang="tl" data-title="Likas na bilang" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%AF%E0%AE%B2%E0%AF%8D_%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="இயல் எண் — тамільская" lang="ta" hreflang="ta" data-title="இயல் எண்" data-language-autonym="தமிழ்" data-language-local-name="тамільская" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D0%B0%D0%B1%D0%B8%D0%B3%D1%8B%D0%B9_%D1%81%D0%B0%D0%BD" title="Табигый сан — татарская" lang="tt" hreflang="tt" data-title="Табигый сан" data-language-autonym="Татарча / tatarça" data-language-local-name="татарская" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B0%B9%E0%B0%9C_%E0%B0%B8%E0%B0%82%E0%B0%96%E0%B1%8D%E0%B0%AF" title="సహజ సంఖ్య — тэлуская" lang="te" hreflang="te" data-title="సహజ సంఖ్య" data-language-autonym="తెలుగు" data-language-local-name="тэлуская" 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%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%98%E0%B8%A3%E0%B8%A3%E0%B8%A1%E0%B8%8A%E0%B8%B2%E0%B8%95%E0%B8%B4" title="จำนวนธรรมชาติ — тайская" lang="th" hreflang="th" data-title="จำนวนธรรมชาติ" data-language-autonym="ไทย" data-language-local-name="тайская" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%B4%D0%B0%D0%B4%D0%B8_%D0%BD%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D3%A3" title="Адади натуралӣ — таджыцкая" lang="tg" hreflang="tg" data-title="Адади натуралӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="таджыцкая" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Do%C4%9Fal_say%C4%B1lar" title="Doğal sayılar — турэцкая" lang="tr" hreflang="tr" data-title="Doğal sayılar" data-language-autonym="Türkçe" data-language-local-name="турэцкая" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Natural_sanlar" title="Natural sanlar — туркмэнская" lang="tk" hreflang="tk" data-title="Natural sanlar" data-language-autonym="Türkmençe" data-language-local-name="туркмэнская" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-kcg mw-list-item"><a href="https://kcg.wikipedia.org/wiki/A%CC%B1za%CC%B1za%CC%B1rak_la%CC%B1mba" title="A̱za̱za̱rak la̱mba — т’япская" lang="kcg" hreflang="kcg" data-title="A̱za̱za̱rak la̱mba" data-language-autonym="Tyap" data-language-local-name="т’япская" class="interlanguage-link-target"><span>Tyap</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Натуральне число — украінская" lang="uk" hreflang="uk" data-title="Натуральне число" data-language-autonym="Українська" data-language-local-name="украінская" 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/%D9%82%D8%AF%D8%B1%D8%AA%DB%8C_%D8%B9%D8%AF%D8%AF" title="قدرتی عدد — урду" lang="ur" hreflang="ur" data-title="قدرتی عدد" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91_t%E1%BB%B1_nhi%C3%AAn" title="Số tự nhiên — віетнамская" lang="vi" hreflang="vi" data-title="Số tự nhiên" data-language-autonym="Tiếng Việt" data-language-local-name="віетнамская" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/T%C3%BCk%C3%BCarv" title="Tüküarv — Võro" lang="vro" hreflang="vro" data-title="Tüküarv" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E6%95%B8" title="自然數 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="自然數" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Natuurlik_getal" title="Natuurlik getal — West Flemish" lang="vls" hreflang="vls" data-title="Natuurlik getal" 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-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Unob_nga_ihap" title="Unob nga ihap — варайская" lang="war" hreflang="war" data-title="Unob nga ihap" data-language-autonym="Winaray" data-language-local-name="варайская" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E6%95%B0" title="自然数 — ву" lang="wuu" hreflang="wuu" data-title="自然数" data-language-autonym="吴语" data-language-local-name="ву" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A0%D7%90%D7%98%D7%99%D7%A8%D7%9C%D7%A2%D7%9B%D7%A2_%D7%A6%D7%90%D7%9C" title="נאטירלעכע צאל — ідыш" lang="yi" hreflang="yi" data-title="נאטירלעכע צאל" data-language-autonym="ייִדיש" data-language-local-name="ідыш" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/N%E1%BB%8D%CC%81mb%C3%A0_%C3%A0d%C3%A1b%C3%A1y%C3%A9" title="Nọ́mbà àdábáyé — ёрубская" lang="yo" hreflang="yo" data-title="Nọ́mbà àdábáyé" data-language-autonym="Yorùbá" data-language-local-name="ёрубская" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E6%95%B8" title="自然數 — кантонская" lang="yue" hreflang="yue" data-title="自然數" data-language-autonym="粵語" data-language-local-name="кантонская" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Nat%C5%ABral%C4%97%CC%84j%C4%97_skaitl%C4%93" title="Natūralė̄jė skaitlē — Samogitian" lang="sgs" hreflang="sgs" data-title="Natūralė̄jė skaitlē" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E6%95%B0" title="自然数 — кітайская" lang="zh" hreflang="zh" data-title="自然数" data-language-autonym="中文" data-language-local-name="кітайская" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%93%E2%B5%8E%E2%B5%8E%E2%B5%89%E2%B4%B7_%E2%B4%B0%E2%B4%B3%E2%B4%B0%E2%B5%8E%E2%B4%B0%E2%B5%8F" title="ⵓⵎⵎⵉⴷ ⴰⴳⴰⵎⴰⵏ — стандартная мараканская тамазіхт" lang="zgh" hreflang="zgh" data-title="ⵓⵎⵎⵉⴷ ⴰⴳⴰⵎⴰⵏ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="стандартная мараканская тамазіхт" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</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/Q21199#sitelinks-wikipedia" title="Рэдагаваць міжмоўныя спасылкі" class="wbc-editpage">Правіць спасылкі</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="Прасторы назваў"> <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/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Паказаць зьмест старонкі [c]" accesskey="c"><span>Артыкул</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%D0%90%D0%B1%D0%BC%D0%B5%D1%80%D0%BA%D0%B0%D0%B2%D0%B0%D0%BD%D1%8C%D0%BD%D0%B5:%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" rel="discussion" title="Абмеркаваньне зьместу старонкі [t]" accesskey="t"><span>Абмеркаваньне</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="Зьмяніць варыянт мовы" > <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">беларуская (тарашкевіца)</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="Рэжымы"> <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/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA"><span>Чытаць</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&veaction=edit" title="Рэдагаваць гэтую старонку [v]" accesskey="v"><span>Рэдагаваць</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit" title="Рэдагаваць крынічны тэкст гэтай старонкі [e]" accesskey="e"><span>Рэдагаваць крыніцу</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=history" title="Мінулыя вэрсіі гэтай старонкі. [h]" accesskey="h"><span>Паказаць гісторыю</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Інструмэнты" > <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">Інструмэнты</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">Інструмэнты</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">перанесьці ў бакавую панэль</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">схаваць</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Болей вопцыяў" > <div class="vector-menu-heading"> Дзеяньні </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/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA"><span>Чытаць</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&veaction=edit" title="Рэдагаваць гэтую старонку [v]" accesskey="v"><span>Рэдагаваць</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit" title="Рэдагаваць крынічны тэкст гэтай старонкі [e]" accesskey="e"><span>Рэдагаваць крыніцу</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=history"><span>Паказаць гісторыю</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Агульныя </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%A1%D0%BF%D0%B0%D1%81%D1%8B%D0%BB%D0%BA%D1%96_%D0%BD%D0%B0_%D1%81%D1%82%D0%B0%D1%80%D0%BE%D0%BD%D0%BA%D1%83/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Сьпіс усіх старонак, якія спасылаюцца на гэтую [j]" accesskey="j"><span>Спасылкі на старонку</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:RecentChangesLinked/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" rel="nofollow" title="Апошнія зьмены ў старонках, на якія спасылаецца гэтая старонка [k]" accesskey="k"><span>Зьвязаныя 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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">Выгляд</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">перанесьці ў бакавую панэль</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">схаваць</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">Зьвесткі зь Вікіпэдыі — вольнай энцыкляпэдыі</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="be-tarask" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Three_apples.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Three_apples.svg/220px-Three_apples.svg.png" decoding="async" width="220" height="265" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Three_apples.svg/330px-Three_apples.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Three_apples.svg/440px-Three_apples.svg.png 2x" data-file-width="512" data-file-height="616" /></a><figcaption>Натуральныя лікі можна выкарыстоўваць пры лічэньні (адзін яблык, два яблыкі, тры яблыкі, …)</figcaption></figure> <p><b>Натуральныя лікі</b> — элемэнты бясконцага <a href="/wiki/%D0%9C%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0" title="Мноства">мноства</a> {1, 2, 3, 4…}. Гэта мноства называецца <b>натуральны шэраг</b>. Яго вывучаюць <a href="/wiki/%D0%90%D1%80%D1%8B%D1%82%D0%BC%D1%8D%D1%82%D1%8B%D0%BA%D0%B0" title="Арытмэтыка">арытмэтыка</a>, <a href="/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D0%B0%D1%9E" title="Тэорыя лікаў">тэорыя лікаў</a> і <a href="/wiki/%D0%9A%D0%B0%D0%BC%D0%B1%D1%96%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D1%8B%D0%BA%D0%B0" title="Камбінаторыка">камбінаторыка</a>. </p><p>У некаторых навуках (<a href="/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0%D1%9E" title="Тэорыя мностваў">тэорыі мностваў</a>, <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D0%BB%D1%91%D0%B3%D1%96%D0%BA%D0%B0" title="Матэматычная лёгіка">матэматычнай лёгіцы</a>, <a href="/wiki/%D0%86%D0%BD%D1%84%D0%B0%D1%80%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Інфарматыка">інфарматыцы</a>) выкарыстоўваюць г. зв. «пашыраны натуральны шэраг» {0, 1, 2, 3, 4…}. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Гісторыя"><span id=".D0.93.D1.96.D1.81.D1.82.D0.BE.D1.80.D1.8B.D1.8F"></span>Гісторыя</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&veaction=edit&section=1" title="Рэдагаваць сэкцыю «Гісторыя»" class="mw-editsection-visualeditor"><span>рэдагаваць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&section=1" title="Правіць зыходнік раздзела: Гісторыя"><span>рэдагаваць крыніцу</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Патрэбнасьць у натуральных ліках узьнікла пры лічэньні прадметаў. Лік «два» зьвязваўся з органамі зроку і слыху і ўвогуле з канкрэтнай парай рэчаў. «Вочы» ў <a href="/wiki/%D0%86%D0%BD%D0%B4%D1%8B%D0%B9%D1%86%D1%8B" title="Індыйцы">індыйцаў</a>, «Крылы» ў <a href="/w/index.php?title=%D0%A2%D1%8B%D0%B1%D1%8D%D1%82%D1%86%D1%8B&action=edit&redlink=1" class="new" title="Тыбэтцы (старонка не існуе)">тыбэтцаў</a> азначалі таксама «два». З-за неабходнасьці весьці лік любых групаў прадметаў і ўзьніклі натуральныя лікі: адзін, два, тры і г. д. Калі пазьней для падліку сталі выкарыстоўваць «эталённыя мноствы» — зарубкі, вузлы на вяроўках, каменьчыкі — узьнікла абстрактнае ўяўленьне ліку. На першых стадыях культурнага разьвіцьця чалавецтва натуральны шэраг складаўся зь нямногіх лікаў. Паступова ён абагачаўся ўсё новымі і большымі лікамі. </p><p>Аднак доўгі час натуральны шэраг лічыўся канечным, то бок людзі лічылі, што існуе нейкі апошні, найбольшы лік. І толькі ў <a href="/wiki/3_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B7%D1%8C%D0%B4%D0%B7%D0%B5_%D0%B4%D0%B0_%D0%BD._%D1%8D." class="mw-redirect" title="3 стагодзьдзе да н. э.">III стагодзьдзі да н. э.</a> <a href="/wiki/%D0%90%D1%80%D1%85%D1%96%D0%BC%D1%8D%D0%B4" title="Архімэд">Архімэд</a> у невялікай арытмэтычнай кнізе “Псамміт” паказаў, што падлік можна працягваць бязьмежна, гэта значыць, натуральны шэраг бясконцы. <a href="/wiki/%D0%AD%D1%9E%D0%BA%D0%BB%D1%96%D0%B4" title="Эўклід">Эўклід</a> яшчэ ў <a href="/wiki/3_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B7%D1%8C%D0%B4%D0%B7%D0%B5_%D0%B4%D0%B0_%D0%BD._%D1%8D." class="mw-redirect" title="3 стагодзьдзе да н. э.">III стагодзьдзі да н. э.</a> вызначаў натуральны лік як “мноства складзенае з адзінак”. Аб натуральным у сэнсе прыродным шэрагу лікаў гаворыцца ва “Ўводзінах у арытмэтыку” <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%80%D0%B0%D0%B6%D1%8B%D1%82%D0%BD%D0%B0%D1%8F_%D0%93%D1%80%D1%8D%D1%86%D1%8B%D1%8F" title="Старажытная Грэцыя">грэцкага</a> матэматыка (<a href="/w/index.php?title=%D0%9D%D1%8D%D0%B0%D0%BF%D1%96%D1%82%D0%B0%D0%B3%D0%B0%D1%80%D1%8D%D0%B9%D1%86%D1%8B&action=edit&redlink=1" class="new" title="Нэапітагарэйцы (старонка не існуе)">нэапітагарэйца</a>) <a href="/w/index.php?title=%D0%9D%D1%96%D0%BA%D0%B0%D0%BC%D0%B0%D1%85%D0%B7_%D0%93%D0%B5%D1%80%D0%B0%D0%B7%D1%8B&action=edit&redlink=1" class="new" title="Нікамахз Геразы (старонка не існуе)">Нікамах з Геразы</a>, які жыў каля <a href="/wiki/100" title="100">100 г. н. э.</a> Арытмэтыка Нікамаха была перапрацавана і перакладзена на <a href="/wiki/%D0%9B%D0%B0%D1%86%D1%96%D0%BD%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B2%D0%B0" title="Лацінская мова">латцінскую мову</a> <a href="/w/index.php?title=%D0%A0%D1%8B%D0%BC%D1%81&action=edit&redlink=1" class="new" title="Рымс (старонка не існуе)">рымскім</a> аўтарам <a href="/w/index.php?title=%D0%91%D0%B0%D1%8D%D1%86%D1%8B%D0%B9&action=edit&redlink=1" class="new" title="Баэцый (старонка не існуе)">Баэцыем</a> (<a href="/wiki/480" title="480">480</a>—<a href="/wiki/524" title="524">524</a>), які ўпершыню ўжыў тэрмін “Натуральны лік”, які сустракаецца затым ў некаторых сярэднявечных <a href="/wiki/%D0%A0%D1%83%D0%BA%D0%B0%D0%BF%D1%96%D1%81" title="Рукапіс">рукапісах</a>. У сучасным сэнсе азначэньне і тэрмін “натуральнага ліку” сустракаецца ў <a href="/wiki/%D0%A4%D1%80%D0%B0%D0%BD%D1%86%D1%8B%D1%8F" title="Францыя">францускага</a> філёзафа і матэматыка <a href="/wiki/%D0%96%D0%B0%D0%BD_%D0%BB%D1%8F_%D0%A0%D0%BE%D0%BD_%D0%B4%E2%80%99%D0%90%D0%BB%D1%8F%D0%BC%D0%B1%D1%8D%D1%80" title="Жан ля Рон д’Алямбэр">Ж. д’Алямбэра</a> (<a href="/wiki/1717" title="1717">1717</a>—<a href="/wiki/1783" title="1783">1783</a>). </p><p>З-за інтуітыўнай зразумеласьці тэорыяй натуральных лікаў навукоўцы доўга не цікавіліся. У пачатку <a href="/wiki/18_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B7%D1%8C%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="18 стагодзьдзе">18 стагодзьдзя</a> <a href="/w/index.php?title=%D0%93%D0%BE%D1%82%D1%84%D1%80%D1%8B%D0%B4_%D0%92%D1%96%D0%BB%D1%8C%D0%B3%D1%8D%D0%BB%D1%8C%D0%BC_%D0%9B%D1%8F%D0%B9%D0%B1%D0%BD%D1%96%D1%86&action=edit&redlink=1" class="new" title="Готфрыд Вільгэльм Ляйбніц (старонка не існуе)">Ляйбніц</a> паставіў задачу дэдуктыўнай пабудовы <a href="/wiki/%D0%90%D1%80%D1%8B%D1%82%D0%BC%D1%8D%D1%82%D1%8B%D0%BA%D0%B0" title="Арытмэтыка">арытметыкі</a>. Глыбокае дасьледаваньне правёў <a href="/w/index.php?title=%D0%93%D1%8D%D1%80%D0%BC%D0%B0%D0%BD_%D0%93%D1%8E%D0%BD%D1%82%D1%8D%D1%80_%D0%93%D1%80%D0%B0%D1%81%D0%BC%D0%B0%D0%BD&action=edit&redlink=1" class="new" title="Гэрман Гюнтэр Грасман (старонка не існуе)">Грасман</a> толькі ў <a href="/wiki/1861" title="1861">1861</a>, а поўную сыстэму прапанаваў <a href="/w/index.php?title=%D0%94%D0%B6%D1%83%D0%B7%D1%8D%D0%BF%D0%B0_%D0%9F%D1%8D%D0%B0%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Джузэпа Пэана (старонка не існуе)">Пэана</a> ў <a href="/wiki/1889" title="1889">1889</a>. </p><p>У <a href="/wiki/1878" title="1878">1878</a> <a href="/w/index.php?title=%D0%93%D1%8D%D0%BE%D1%80%D0%B3_%D0%9A%D0%B0%D0%BD%D1%82%D0%B0%D1%80&action=edit&redlink=1" class="new" title="Гэорг Кантар (старонка не існуе)">Кантар</a> увёў паняцьце "<a href="/w/index.php?title=%D0%9C%D0%B0%D0%B3%D1%83%D1%82%D0%BD%D0%B0%D1%81%D1%8C%D1%86%D1%8C_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0&action=edit&redlink=1" class="new" title="Магутнасьць мноства (старонка не існуе)">магутнасьці мноства</a>", падзяліў лікі на "ардынальныя" і "<a href="/w/index.php?title=%D0%9A%D0%B0%D0%B0%D1%80%D0%B4%D1%8B%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&redlink=1" class="new" title="Каардынальны лік (старонка не існуе)">каардынальныя</a>", у <a href="/wiki/1900" title="1900">1900</a> <a href="/w/index.php?title=%D0%94%D0%B0%D0%B2%D1%8B%D0%B4_%D0%93%D1%96%D0%BB%D1%8C%D0%B1%D1%8D%D1%80%D1%82&action=edit&redlink=1" class="new" title="Давыд Гільбэрт (старонка не існуе)">Гільбэрт</a> зрабіў шэраг спроб скончыць працу, а ў <a href="/wiki/1932" title="1932">1932</a> <a href="/wiki/%D0%9A%D1%83%D1%80%D1%82_%D0%93%D1%91%D0%B4%D1%8D%D0%BB%D1%8C" title="Курт Гёдэль">Гёдэль</a> паказаў, што нельга даць скончаную лягічную пабудову арытмэтыкі на аснове сыстэмы <a href="/wiki/%D0%90%D0%BA%D1%81%D1%8B%D1%91%D0%BC%D0%B0" class="mw-redirect" title="Аксыёма">аксіём</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Аксіёматычнае_ўвядзеньне_Пэана"><span id=".D0.90.D0.BA.D1.81.D1.96.D1.91.D0.BC.D0.B0.D1.82.D1.8B.D1.87.D0.BD.D0.B0.D0.B5_.D1.9E.D0.B2.D1.8F.D0.B4.D0.B7.D0.B5.D0.BD.D1.8C.D0.BD.D0.B5_.D0.9F.D1.8D.D0.B0.D0.BD.D0.B0"></span>Аксіёматычнае ўвядзеньне Пэана</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&veaction=edit&section=2" title="Рэдагаваць сэкцыю «Аксіёматычнае ўвядзеньне Пэана»" class="mw-editsection-visualeditor"><span>рэдагаваць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&section=2" title="Правіць зыходнік раздзела: Аксіёматычнае ўвядзеньне Пэана"><span>рэдагаваць крыніцу</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Натуральнымі лікамі называюцца элемэнты ўсякага непустога мноства <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>, у якім для нейкіх элемэнтаў <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> і <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> існуе адносіна "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> накіроўваецца за <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> (пазначаецца як <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cb64c0f02687512818f37839ce23ee049c37743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.915ex; height:2.509ex;" alt="{\displaystyle a'}"></span>) і задавальняе наступным <a href="/wiki/%D0%90%D0%BA%D1%81%D1%96%D1%91%D0%BC%D0%B0" title="Аксіёма">аксіёмам</a>, якія атрымалі назву <a href="/wiki/%D0%90%D0%BA%D1%81%D1%96%D1%91%D0%BC%D1%8B_%D0%9F%D1%8D%D0%B0%D0%BD%D0%B0" title="Аксіёмы Пэана">аксіёмаў Пэана</a>: </p> <ol><li>існуе 1, якое не накіроўваецца ні за ніводным элемэнтам,</li> <li>для любога <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> існуе <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cb64c0f02687512818f37839ce23ee049c37743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.915ex; height:2.509ex;" alt="{\displaystyle a'}"></span>, якое накіроўваецца за ім, прычым толькі адно,</li> <li>любы элемэнт накіроўваецца ня больш чым за адным элемэнтам,</li> <li>любое мноства <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 {M} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c466bc0f750f74236f81922b9bff54b6d50452a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.194ex; height:2.176ex;" alt="{\displaystyle \mathbb {M} }"></span> з уласьцівасьцямі <ul><li>1 прыналежыць <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 {M} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c466bc0f750f74236f81922b9bff54b6d50452a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.194ex; height:2.176ex;" alt="{\displaystyle \mathbb {M} }"></span>,</li> <li>калі <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> прыналежыць <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 {M} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c466bc0f750f74236f81922b9bff54b6d50452a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.194ex; height:2.176ex;" alt="{\displaystyle \mathbb {M} }"></span>, то і <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cb64c0f02687512818f37839ce23ee049c37743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.915ex; height:2.509ex;" alt="{\displaystyle a'}"></span> прыналежыць <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 {M} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">M</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {M} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c466bc0f750f74236f81922b9bff54b6d50452a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.194ex; height:2.176ex;" alt="{\displaystyle \mathbb {M} }"></span></li></ul></li></ol> <p>- супадае з <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> (аксіёма <a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D1%96%D0%BD%D0%B4%D1%83%D0%BA%D1%86%D1%8B%D1%8F&action=edit&redlink=1" class="new" title="Матэматычная індукцыя (старонка не існуе)">індукцыі</a>) </p><p>На гэтам мностве можна ўвесьці апэрацыі <a href="/wiki/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%B0%D0%BD%D1%8C%D0%BD%D0%B5" title="Складаньне">складаньня</a> й <a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B0%D0%BD%D1%8C%D0%BD%D0%B5" title="Множаньне">множаньня</a>. </p><p>Складаньне - гэта апэрацыя з уласьцівасьцямі: </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a+1=a'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>+</mo> <mn>1</mn> <mo>=</mo> <msup> <mi>a</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a+1=a'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/194e51be91c0ae1bceba71955e25e1ab14bdc203" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.246ex; height:2.676ex;" alt="{\displaystyle a+1=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+b'=(a+b)'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>+</mo> <msup> <mi>b</mi> <mo>′</mo> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a+b'=(a+b)'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2bfbcf65bb5da7044f244a257cf2cf1139cd595" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.413ex; height:3.009ex;" alt="{\displaystyle a+b'=(a+b)'}"></span></li></ol> <p>Множаньне - гэта апэрацыя з уласьцівасьцямі: </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\times 1=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>×</mo> <mn>1</mn> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\times 1=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04e0634cfe81c515b29a69b624960f73b8167e60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.561ex; height:2.176ex;" alt="{\displaystyle a\times 1=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\times b'=a\times b+a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>×</mo> <msup> <mi>b</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>a</mi> <mo>×</mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\times b'=a\times b+a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49d2b15f63c6a0a6a69c8330ae318a38762a36a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:17.989ex; height:2.676ex;" alt="{\displaystyle a\times b'=a\times b+a}"></span></li></ol> <div class="mw-heading mw-heading2"><h2 id="Тэарэтыка-мноственнае_ўвядзеньне"><span id=".D0.A2.D1.8D.D0.B0.D1.80.D1.8D.D1.82.D1.8B.D0.BA.D0.B0-.D0.BC.D0.BD.D0.BE.D1.81.D1.82.D0.B2.D0.B5.D0.BD.D0.BD.D0.B0.D0.B5_.D1.9E.D0.B2.D1.8F.D0.B4.D0.B7.D0.B5.D0.BD.D1.8C.D0.BD.D0.B5"></span>Тэарэтыка-мноственнае ўвядзеньне</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&veaction=edit&section=3" title="Рэдагаваць сэкцыю «Тэарэтыка-мноственнае ўвядзеньне»" class="mw-editsection-visualeditor"><span>рэдагаваць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&section=3" title="Правіць зыходнік раздзела: Тэарэтыка-мноственнае ўвядзеньне"><span>рэдагаваць крыніцу</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Пашыраны натуральны шэраг можна ўвесьці як <a href="/wiki/%D0%9C%D0%B0%D0%B3%D1%83%D1%82%D0%BD%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Магутнасьць">магутнасьць</a> канечнага мноства. У адрозьненьне ад аксіёматыкі Пэаны, натуральныя лікі тут азначаюць не парадак, а колькасьць. Вось прыклад такога азначэньня: </p> <dl><dd><ul><li>0 = { }</li> <li>1 = {0} = {{ }}</li> <li>2 = {0,1} = {0, {0}} = {{ }, {{ }}}</li> <li>3 = {0,1,2} = {0, {0}, {0, {0}}} = {{ }, {{ }}, {{ }, {{ }}}}</li> <li><i>n</i> = {0,1,2,...,<i>n</i>−2,<i>n</i>−1} = {0,1,2,...,<i>n</i>−2} ∪ {<i>n</i>−1} = (<i>n</i>−1) ∪ {<i>n</i>−1}</li></ul></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Уласьцівасьці"><span id=".D0.A3.D0.BB.D0.B0.D1.81.D1.8C.D1.86.D1.96.D0.B2.D0.B0.D1.81.D1.8C.D1.86.D1.96"></span>Уласьцівасьці</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&veaction=edit&section=4" title="Рэдагаваць сэкцыю «Уласьцівасьці»" class="mw-editsection-visualeditor"><span>рэдагаваць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&section=4" title="Правіць зыходнік раздзела: Уласьцівасьці"><span>рэдагаваць крыніцу</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Мноства натуральных лікаў <a href="/w/index.php?title=%D0%97%D1%8C%D0%BB%D1%96%D1%87%D0%B0%D0%BD%D0%B0%D0%B5_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0&action=edit&redlink=1" class="new" title="Зьлічанае мноства (старонка не існуе)">зьлічальнае</a>, абмежаванае зьнізу. На ім вызначаныя <a href="/w/index.php?title=%D0%9F%D0%BE%D1%9E%D0%BD%D1%8B_%D0%BF%D0%B0%D1%80%D0%B0%D0%B4%D0%B0%D0%BA&action=edit&redlink=1" class="new" title="Поўны парадак (старонка не існуе)">поўны парадак</a>, апэрацыі <a href="/wiki/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%B0%D0%BD%D1%8C%D0%BD%D0%B5" title="Складаньне">складаньне</a> й <a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B0%D0%BD%D1%8C%D0%BD%D0%B5" title="Множаньне">множаньне</a> (для ўсіх лікаў), <a href="/wiki/%D0%90%D0%B4%D1%8B%D0%BC%D0%B0%D0%BD%D1%8C%D0%BD%D0%B5" title="Адыманьне">адыманьне</a> й <a href="/wiki/%D0%94%D0%B7%D1%8F%D0%BB%D0%B5%D0%BD%D1%8C%D0%BD%D0%B5" title="Дзяленьне">дзяленьне</a> (не для ўсіх лікаў). </p> <div class="mw-heading mw-heading2"><h2 id="Літаратура"><span id=".D0.9B.D1.96.D1.82.D0.B0.D1.80.D0.B0.D1.82.D1.83.D1.80.D0.B0"></span>Літаратура</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&veaction=edit&section=5" title="Рэдагаваць сэкцыю «Літаратура»" class="mw-editsection-visualeditor"><span>рэдагаваць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&section=5" title="Правіць зыходнік раздзела: Літаратура"><span>рэдагаваць крыніцу</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Энциклопедия элементарной математики под редакцией П.С. Александрова, А.И. Маркушевича и А.Я. Хинчина</i></li> <li><i>История математики с древнейших времён до начала XIX столетия под редакцией А.П. Юшкевич</i></li> <li><i>Зорич В. А. Математический анализ. Часть І.</i></li> <li><i>Выгодский М.Я. Справочник по элементарной математике.</i></li> <li><i>Глейзер Г. И. История математики в школе.</i></li> <li><i>Р. Курант, Г. Роббинс. Что такое математика?</i></li></ul> <table class="metadata plainlinks stub" style="background: transparent;"><tbody><tr> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Antu_accessories-calculator.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Antu_accessories-calculator.svg/40px-Antu_accessories-calculator.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Antu_accessories-calculator.svg/60px-Antu_accessories-calculator.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Antu_accessories-calculator.svg/80px-Antu_accessories-calculator.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></td> <td><i>Гэта — <a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D1%8D%D0%B4%D1%8B%D1%8F:%D0%9D%D0%B0%D0%BA%D1%96%D0%B4" title="Вікіпэдыя:Накід">накід</a> артыкула па <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Матэматыка">матэматыцы</a>. Вы можаце дапамагчы Вікіпэдыі, <a class="external text" href="https://be-tarask.wikipedia.org/w/index.php?title=%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit">пашырыўшы яго</a>.</i></td> </tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Атрымана з «<a dir="ltr" href="https://be-tarask.wikipedia.org/w/index.php?title=Натуральны_лік&oldid=1947510">https://be-tarask.wikipedia.org/w/index.php?title=Натуральны_лік&oldid=1947510</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F:%D0%9A%D0%B0%D1%82%D1%8D%D0%B3%D0%BE%D1%80%D1%8B%D1%96" title="Спэцыяльныя:Катэгорыі">Катэгорыя</a>: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D1%8D%D0%B3%D0%BE%D1%80%D1%8B%D1%8F:%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96" title="Катэгорыя:Натуральныя лікі">Натуральныя лікі</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Схаваная катэгорыя: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D1%8D%D0%B3%D0%BE%D1%80%D1%8B%D1%8F:%D0%92%D1%96%D0%BA%D1%96%D0%BF%D1%8D%D0%B4%D1%8B%D1%8F:%D0%9D%D0%B0%D0%BA%D1%96%D0%B4%D1%8B:%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Катэгорыя:Вікіпэдыя:Накіды:Матэматыка">Вікіпэдыя:Накіды:Матэматыка</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"> Гэтая старонка апошні раз рэдагавалася 29 сьнежня 2017 году ў 11:04.</li> <li id="footer-info-copyright">Гэты тэкст даступны на ўмовах <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.be">ліцэнзіі Creative Commons Attribution/Share-Alike 4.0</a>; 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