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[o]" accesskey="o"> Увайсці</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 ананімных рэдактараў <a href="/wiki/%D0%94%D0%B0%D0%B2%D0%B5%D0%B4%D0%BA%D0%B0:%D0%94%D0%B0%D0%B2%D0%B5%D0%B4%D0%BA%D0%B0" aria-label="Даведацца больш пра праўку">даведацца больш</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%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:MyContributions" title="Спіс правак, зробленых з гэтага IP-адраса [y]" accesskey="y">Уклад</a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:MyTalk" title="Размовы пра праўкі, зробленыя з гэтага IP-адраса [n]" accesskey="n">Размовы</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="Праект"> <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="Змест" 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">Змест</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">перанесці да бакавой панэлі</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-Асноўныя_ўласцівасці_нуля" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Асноўныя_ўласцівасці_нуля"> <div class="vector-toc-text"> 1 Асноўныя ўласцівасці нуля </div> </a> <button aria-controls="toc-Асноўныя_ўласцівасці_нуля-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Змяніць стан падраздзелу Асноўныя ўласцівасці нуля </button> <ul id="toc-Асноўныя_ўласцівасці_нуля-sublist" class="vector-toc-list"> <li id="toc-Абагульненні" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Абагульненні"> <div class="vector-toc-text"> 1.1 Абагульненні </div> </a> <ul id="toc-Абагульненні-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Адносіны_да_натуральных_лікаў" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Адносіны_да_натуральных_лікаў"> <div class="vector-toc-text"> 2 Адносіны да натуральных лікаў </div> </a> <ul id="toc-Адносіны_да_натуральных_лікаў-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ужыванне" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ужыванне"> <div class="vector-toc-text"> 3 Ужыванне </div> </a> <button aria-controls="toc-Ужыванне-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Змяніць стан падраздзелу Ужыванне </button> <ul id="toc-Ужыванне-sublist" class="vector-toc-list"> <li id="toc-У_матэматыцы" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#У_матэматыцы"> <div class="vector-toc-text"> 3.1 У матэматыцы </div> </a> <ul id="toc-У_матэматыцы-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-У_фізіцы" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#У_фізіцы"> <div class="vector-toc-text"> 3.2 У фізіцы </div> </a> <ul id="toc-У_фізіцы-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-У_іншых_галінах" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#У_іншых_галінах"> <div class="vector-toc-text"> 3.3 У іншых галінах </div> </a> <ul id="toc-У_іншых_галінах-sublist" class="vector-toc-list"> </ul> </li> </ul> </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"> 4 Гісторыя </div> </a> <button aria-controls="toc-Гісторыя-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Змяніць стан падраздзелу Гісторыя </button> <ul id="toc-Гісторыя-sublist" class="vector-toc-list"> <li id="toc-Старажытны_Блізкі_Усход" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Старажытны_Блізкі_Усход"> <div class="vector-toc-text"> 4.1 Старажытны Блізкі Усход </div> </a> <ul id="toc-Старажытны_Блізкі_Усход-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Дакалумбава_Амерыка" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Дакалумбава_Амерыка"> <div class="vector-toc-text"> 4.2 Дакалумбава Амерыка </div> </a> <ul id="toc-Дакалумбава_Амерыка-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Класічная_антычнасць" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Класічная_антычнасць"> <div class="vector-toc-text"> 4.3 Класічная антычнасць </div> </a> <ul id="toc-Класічная_антычнасць-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Кітай" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Кітай"> <div class="vector-toc-text"> 4.4 Кітай </div> </a> <ul id="toc-Кітай-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Індыя" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Індыя"> <div class="vector-toc-text"> 4.5 Індыя </div> </a> <ul id="toc-Індыя-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Сярэднявечча" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Сярэднявечча"> <div class="vector-toc-text"> 4.6 Сярэднявечча </div> </a> <ul id="toc-Сярэднявечча-sublist" class="vector-toc-list"> <li id="toc-З'яўленне_ў_ісламскім_свеце" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#З'яўленне_ў_ісламскім_свеце"> <div class="vector-toc-text"> 4.6.1 З'яўленне ў ісламскім свеце </div> </a> <ul id="toc-З'яўленне_ў_ісламскім_свеце-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-З'яўленне_ў_Еўропе" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#З'яўленне_ў_Еўропе"> <div class="vector-toc-text"> 4.6.2 З'яўленне ў Еўропе </div> </a> <ul id="toc-З'яўленне_ў_Еўропе-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Гл._таксама" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Гл._таксама"> <div class="vector-toc-text"> 5 Гл. таксама </div> </a> <ul id="toc-Гл._таксама-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Заўвагі" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Заўвагі"> <div class="vector-toc-text"> 6 Заўвагі </div> </a> <ul id="toc-Заўвагі-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Зноскі" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Зноскі"> <div class="vector-toc-text"> 7 Зноскі </div> </a> <ul id="toc-Зноскі-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Спасылкі" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Спасылкі"> <div class="vector-toc-text"> 8 Спасылкі </div> </a> <ul id="toc-Спасылкі-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="Змест" 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="Пераключыць змест" > <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" > Пераключыць змест </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">0 (лік)</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="Перайсці да артыкула на іншай мове. Даступны на 156 мовах." > <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-156" aria-hidden="true" > 156 моў </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ab mw-list-item"><a href="https://ab.wikipedia.org/wiki/%D0%90%D0%BD%D0%BE%D0%BB%D1%8C" title="Аноль – абхазская" lang="ab" hreflang="ab" data-title="Аноль" data-language-autonym="Аԥсшәа" data-language-local-name="абхазская" class="interlanguage-link-target">Аԥсшәа</a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/0_(getal)" title="0 (getal) – афрыкаанс" lang="af" hreflang="af" data-title="0 (getal)" data-language-autonym="Afrikaans" data-language-local-name="афрыкаанс" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Null" title="Null – швейцарская нямецкая" lang="gsw" hreflang="gsw" data-title="Null" data-language-autonym="Alemannisch" data-language-local-name="швейцарская нямецкая" class="interlanguage-link-target">Alemannisch</a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/0" title="0 – амхарская" lang="am" hreflang="am" data-title="0" data-language-autonym="አማርኛ" data-language-local-name="амхарская" class="interlanguage-link-target">አማርኛ</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/0_(%D8%B9%D8%AF%D8%AF)" title="0 (عدد) – арабская" lang="ar" hreflang="ar" data-title="0 (عدد)" data-language-autonym="العربية" data-language-local-name="арабская" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-arc mw-list-item"><a href="https://arc.wikipedia.org/wiki/0_(%DC%A1%DC%A2%DC%9D%DC%A2%DC%90)" title="0 (ܡܢܝܢܐ) – арамейская" lang="arc" hreflang="arc" data-title="0 (ܡܢܝܢܐ)" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="арамейская" class="interlanguage-link-target">ܐܪܡܝܐ</a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/0" title="0 – Moroccan Arabic" lang="ary" hreflang="ary" data-title="0" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target">الدارجة</a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B6%E0%A7%82%E0%A6%A8%E0%A7%8D%E0%A6%AF" title="শূন্য – асамская" lang="as" hreflang="as" data-title="শূন্য" data-language-autonym="অসমীয়া" data-language-local-name="асамская" class="interlanguage-link-target">অসমীয়া</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Cero" title="Cero – астурыйская" lang="ast" hreflang="ast" data-title="Cero" data-language-autonym="Asturianu" data-language-local-name="астурыйская" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/0" title="0 – азербайджанская" lang="az" hreflang="az" data-title="0" data-language-autonym="Azərbaycanca" data-language-local-name="азербайджанская" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DB%B0_(%D8%B3%D8%A7%DB%8C%DB%8C)" title="۰ (سایی) – South Azerbaijani" lang="azb" hreflang="azb" data-title="۰ (سایی)" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/0_(%D2%BB%D0%B0%D0%BD)" title="0 (һан) – башкірская" lang="ba" hreflang="ba" data-title="0 (һан)" data-language-autonym="Башҡортса" data-language-local-name="башкірская" class="interlanguage-link-target">Башҡортса</a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/0_(angka)" title="0 (angka) – балійская" lang="ban" hreflang="ban" data-title="0 (angka)" data-language-autonym="Basa Bali" data-language-local-name="балійская" class="interlanguage-link-target">Basa Bali</a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9D%D1%83%D0%BB%D1%8C" title="Нуль – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Нуль" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target">Беларуская (тарашкевіца)</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9D%D1%83%D0%BB%D0%B0" title="Нула – балгарская" lang="bg" hreflang="bg" data-title="Нула" data-language-autonym="Български" data-language-local-name="балгарская" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A7%A6_(%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE)" title="০ (সংখ্যা) – бенгальская" lang="bn" hreflang="bn" data-title="০ (সংখ্যা)" data-language-autonym="বাংলা" data-language-local-name="бенгальская" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BC%A0_(%E0%BD%82%E0%BE%B2%E0%BD%84%E0%BD%A6%E0%BC%8B%E0%BD%80%E0%BC%8D)" title="༠ (གྲངས་ཀ།) – тыбецкая" lang="bo" hreflang="bo" data-title="༠ (གྲངས་ཀ།)" data-language-autonym="བོད་ཡིག" data-language-local-name="тыбецкая" class="interlanguage-link-target">བོད་ཡིག</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/0_(broj)" title="0 (broj) – баснійская" lang="bs" hreflang="bs" data-title="0 (broj)" data-language-autonym="Bosanski" data-language-local-name="баснійская" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Zero" title="Zero – каталанская" lang="ca" hreflang="ca" data-title="Zero" data-language-autonym="Català" data-language-local-name="каталанская" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/0" title="0 – Mindong" lang="cdo" hreflang="cdo" data-title="0" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target">閩東語 / Mìng-dĕ̤ng-ngṳ̄</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%A0_(%DA%98%D9%85%D8%A7%D8%B1%DB%95)" title="٠ (ژمارە) – цэнтральнакурдская" lang="ckb" hreflang="ckb" data-title="٠ (ژمارە)" data-language-autonym="کوردی" data-language-local-name="цэнтральнакурдская" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Nula" title="Nula – чэшская" lang="cs" hreflang="cs" data-title="Nula" data-language-autonym="Čeština" data-language-local-name="чэшская" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/0" title="0 – валійская" lang="cy" hreflang="cy" data-title="0" data-language-autonym="Cymraeg" data-language-local-name="валійская" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/0_(tal)" title="0 (tal) – дацкая" lang="da" hreflang="da" data-title="0 (tal)" data-language-autonym="Dansk" data-language-local-name="дацкая" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Null" title="Null – нямецкая" lang="de" hreflang="de" data-title="Null" data-language-autonym="Deutsch" data-language-local-name="нямецкая" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/0_(%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82)" title="0 (αριθμός) – грэчаская" lang="el" hreflang="el" data-title="0 (αριθμός)" data-language-autonym="Ελληνικά" data-language-local-name="грэчаская" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/0" title="0 – англійская" lang="en" hreflang="en" data-title="0" data-language-autonym="English" data-language-local-name="англійская" class="interlanguage-link-target">English</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Nulo" title="Nulo – эсперанта" lang="eo" hreflang="eo" data-title="Nulo" data-language-autonym="Esperanto" data-language-local-name="эсперанта" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cero" title="Cero – іспанская" lang="es" hreflang="es" data-title="Cero" data-language-autonym="Español" data-language-local-name="іспанская" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Null" title="Null – эстонская" lang="et" hreflang="et" data-title="Null" data-language-autonym="Eesti" data-language-local-name="эстонская" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zero" title="Zero – баскская" lang="eu" hreflang="eu" data-title="Zero" data-language-autonym="Euskara" data-language-local-name="баскская" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B5%D9%81%D8%B1" title="صفر – фарсі" lang="fa" hreflang="fa" data-title="صفر" data-language-autonym="فارسی" data-language-local-name="фарсі" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/0_(luku)" title="0 (luku) – фінская" lang="fi" hreflang="fi" data-title="0 (luku)" data-language-autonym="Suomi" data-language-local-name="фінская" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Saiva" title="Saiva – фіджыйская" lang="fj" hreflang="fj" data-title="Saiva" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="фіджыйская" class="interlanguage-link-target">Na Vosa Vakaviti</a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/0_(tal)" title="0 (tal) – фарэрская" lang="fo" hreflang="fo" data-title="0 (tal)" data-language-autonym="Føroyskt" data-language-local-name="фарэрская" class="interlanguage-link-target">Føroyskt</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Z%C3%A9ro" title="Zéro – французская" lang="fr" hreflang="fr" data-title="Zéro" data-language-autonym="Français" data-language-local-name="французская" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Nol" title="Nol – паўночнафрызская" lang="frr" hreflang="frr" data-title="Nol" data-language-autonym="Nordfriisk" data-language-local-name="паўночнафрызская" class="interlanguage-link-target">Nordfriisk</a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/0_(numar)" title="0 (numar) – фрыульская" lang="fur" hreflang="fur" data-title="0 (numar)" data-language-autonym="Furlan" data-language-local-name="фрыульская" class="interlanguage-link-target">Furlan</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cero" title="Cero – галісійская" lang="gl" hreflang="gl" data-title="Cero" data-language-autonym="Galego" data-language-local-name="галісійская" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Mba%27eve_(papaha)" title="Mba'eve (papaha) – гуарані" lang="gn" hreflang="gn" data-title="Mba'eve (papaha)" data-language-autonym="Avañe'ẽ" data-language-local-name="гуарані" class="interlanguage-link-target">Avañe'ẽ</a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AB%A6_(%E0%AA%B6%E0%AB%82%E0%AA%A8%E0%AB%8D%E0%AA%AF)" title="૦ (શૂન્ય) – гуджараці" lang="gu" hreflang="gu" data-title="૦ (શૂન્ય)" data-language-autonym="ગુજરાતી" data-language-local-name="гуджараці" class="interlanguage-link-target">ગુજરાતી</a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/0_(earroo)" title="0 (earroo) – мэнская" lang="gv" hreflang="gv" data-title="0 (earroo)" data-language-autonym="Gaelg" data-language-local-name="мэнская" class="interlanguage-link-target">Gaelg</a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/0_(al%C6%99alami)" title="0 (alƙalami) – хауса" lang="ha" hreflang="ha" data-title="0 (alƙalami)" data-language-autonym="Hausa" data-language-local-name="хауса" class="interlanguage-link-target">Hausa</a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/0" title="0 – Hakka Chinese" lang="hak" hreflang="hak" data-title="0" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target">客家語 / Hak-kâ-ngî</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/0_(%D7%9E%D7%A1%D7%A4%D7%A8)" title="0 (מספר) – іўрыт" lang="he" hreflang="he" data-title="0 (מספר)" data-language-autonym="עברית" data-language-local-name="іўрыт" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B6%E0%A5%82%E0%A4%A8%E0%A5%8D%E0%A4%AF" title="शून्य – хіндзі" lang="hi" hreflang="hi" data-title="शून्य" data-language-autonym="हिन्दी" data-language-local-name="хіндзі" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Nula" title="Nula – харвацкая" lang="hr" hreflang="hr" data-title="Nula" data-language-autonym="Hrvatski" data-language-local-name="харвацкая" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/0_(nonm)" title="0 (nonm) – гаіцянская крэольская" lang="ht" hreflang="ht" data-title="0 (nonm)" data-language-autonym="Kreyòl ayisyen" data-language-local-name="гаіцянская крэольская" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/0_(sz%C3%A1m)" title="0 (szám) – венгерская" lang="hu" hreflang="hu" data-title="0 (szám)" data-language-autonym="Magyar" data-language-local-name="венгерская" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/0_(%D5%A9%D5%AB%D5%BE)" title="0 (թիվ) – армянская" lang="hy" hreflang="hy" data-title="0 (թիվ)" data-language-autonym="Հայերեն" data-language-local-name="армянская" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/0_(numero)" title="0 (numero) – інтэрлінгва" lang="ia" hreflang="ia" data-title="0 (numero)" data-language-autonym="Interlingua" data-language-local-name="інтэрлінгва" class="interlanguage-link-target">Interlingua</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/0_(angka)" title="0 (angka) – інданезійская" lang="id" hreflang="id" data-title="0 (angka)" data-language-autonym="Bahasa Indonesia" data-language-local-name="інданезійская" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/0_(%C3%93n%C3%BA%E1%BB%8Dg%E1%BB%A5g%E1%BB%A5)" title="0 (Ónúọgụgụ) – ігба" lang="ig" hreflang="ig" data-title="0 (Ónúọgụgụ)" data-language-autonym="Igbo" data-language-local-name="ігба" class="interlanguage-link-target">Igbo</a></li><li class="interlanguage-link interwiki-ik mw-list-item"><a href="https://ik.wikipedia.org/wiki/Kisitchisa%C4%A1vik" title="Kisitchisaġvik – Inupiaq" lang="ik" hreflang="ik" data-title="Kisitchisaġvik" data-language-autonym="Iñupiatun" data-language-local-name="Inupiaq" class="interlanguage-link-target">Iñupiatun</a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%9A%D3%80%D0%BE%D0%BB%D1%85" title="КӀолх – інгушская" lang="inh" hreflang="inh" data-title="КӀолх" data-language-autonym="ГӀалгӀай" data-language-local-name="інгушская" class="interlanguage-link-target">ГӀалгӀай</a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Zero" title="Zero – іда" lang="io" hreflang="io" data-title="Zero" data-language-autonym="Ido" data-language-local-name="іда" class="interlanguage-link-target">Ido</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/N%C3%BAll" title="Núll – ісландская" lang="is" hreflang="is" data-title="Núll" data-language-autonym="Íslenska" data-language-local-name="ісландская" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/0_(numero)" title="0 (numero) – італьянская" lang="it" hreflang="it" data-title="0 (numero)" data-language-autonym="Italiano" data-language-local-name="італьянская" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/0" title="0 – японская" lang="ja" hreflang="ja" data-title="0" data-language-autonym="日本語" data-language-local-name="японская" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/0_(%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%98)" title="0 (რიცხვი) – грузінская" lang="ka" hreflang="ka" data-title="0 (რიცხვი)" data-language-autonym="ქართული" data-language-local-name="грузінская" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kcg mw-list-item"><a href="https://kcg.wikipedia.org/wiki/0" title="0 – т’яп" lang="kcg" hreflang="kcg" data-title="0" data-language-autonym="Tyap" data-language-local-name="т’яп" class="interlanguage-link-target">Tyap</a></li><li class="interlanguage-link interwiki-kge mw-list-item"><a href="https://kge.wikipedia.org/wiki/0" title="0 – Komering" lang="kge" hreflang="kge" data-title="0" data-language-autonym="Kumoring" data-language-local-name="Komering" class="interlanguage-link-target">Kumoring</a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/K%C4%A9b%C5%A9g%C5%A9_(mathabu)" title="Kĩbũgũ (mathabu) – кікуйю" lang="ki" hreflang="ki" data-title="Kĩbũgũ (mathabu)" data-language-autonym="Gĩkũyũ" data-language-local-name="кікуйю" class="interlanguage-link-target">Gĩkũyũ</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/0_(%D1%81%D0%B0%D0%BD)" title="0 (сан) – казахская" lang="kk" hreflang="kk" data-title="0 (сан)" data-language-autonym="Қазақша" data-language-local-name="казахская" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9F%A0" title="០ – кхмерская" lang="km" hreflang="km" data-title="០" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="кхмерская" class="interlanguage-link-target">ភាសាខ្មែរ</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B8%E0%B3%8A%E0%B2%A8%E0%B3%8D%E0%B2%A8%E0%B3%86" title="ಸೊನ್ನೆ – канада" lang="kn" hreflang="kn" data-title="ಸೊನ್ನೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="канада" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/0" title="0 – карэйская" lang="ko" hreflang="ko" data-title="0" data-language-autonym="한국어" data-language-local-name="карэйская" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/0_(%DA%AF%D8%B1%D9%8E%D9%9B%D9%86%D9%9B%D8%AF)" title="0 (گرَٛنٛد) – кашмірская" lang="ks" hreflang="ks" data-title="0 (گرَٛنٛد)" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="кашмірская" class="interlanguage-link-target">कॉशुर / کٲشُر</a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Sifir_(hejmar)" title="Sifir (hejmar) – курдская" lang="ku" hreflang="ku" data-title="Sifir (hejmar)" data-language-autonym="Kurdî" data-language-local-name="курдская" class="interlanguage-link-target">Kurdî</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9D%D3%A9%D0%BB" title="Нөл – кіргізская" lang="ky" hreflang="ky" data-title="Нөл" data-language-autonym="Кыргызча" data-language-local-name="кіргізская" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/0" title="0 – лацінская" lang="la" hreflang="la" data-title="0" data-language-autonym="Latina" data-language-local-name="лацінская" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lbe mw-list-item"><a href="https://lbe.wikipedia.org/wiki/%D0%9D%D0%BE%D0%BB%D1%8C" title="Ноль – Lak" lang="lbe" hreflang="lbe" data-title="Ноль" data-language-autonym="Лакку" data-language-local-name="Lak" class="interlanguage-link-target">Лакку</a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Zeero" title="Zeero – ганда" lang="lg" hreflang="lg" data-title="Zeero" data-language-autonym="Luganda" data-language-local-name="ганда" class="interlanguage-link-target">Luganda</a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/N%C3%B3l" title="Nól – лімбургская" lang="li" hreflang="li" data-title="Nól" data-language-autonym="Limburgs" data-language-local-name="лімбургская" class="interlanguage-link-target">Limburgs</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/N%C3%BCmar_0" title="Nümar 0 – Lombard" lang="lmo" hreflang="lmo" data-title="Nümar 0" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/Lib%C3%BAng%C3%BAtul%C3%BA" title="Libúngútulú – лінгала" lang="ln" hreflang="ln" data-title="Libúngútulú" data-language-autonym="Lingála" data-language-local-name="лінгала" class="interlanguage-link-target">Lingála</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/0_(skai%C4%8Dius)" title="0 (skaičius) – літоўская" lang="lt" hreflang="lt" data-title="0 (skaičius)" data-language-autonym="Lietuvių" data-language-local-name="літоўская" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Nulle" title="Nulle – латышская" lang="lv" hreflang="lv" data-title="Nulle" data-language-autonym="Latviešu" data-language-local-name="латышская" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%B6%E0%A5%82%E0%A4%A8%E0%A5%8D%E0%A4%AF" title="शून्य – майтхілі" lang="mai" hreflang="mai" data-title="शून्य" data-language-autonym="मैथिली" data-language-local-name="майтхілі" class="interlanguage-link-target">मैथिली</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/0_(%D0%B1%D1%80%D0%BE%D1%98)" title="0 (број) – македонская" lang="mk" hreflang="mk" data-title="0 (број)" data-language-autonym="Македонски" data-language-local-name="македонская" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%82%E0%B4%9C%E0%B5%8D%E0%B4%AF%E0%B4%82" title="പൂജ്യം – малаялам" lang="ml" hreflang="ml" data-title="പൂജ്യം" data-language-autonym="മലയാളം" data-language-local-name="малаялам" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%B0" title="꯰ – мейтэй" lang="mni" hreflang="mni" data-title="꯰" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="мейтэй" class="interlanguage-link-target">ꯃꯤꯇꯩ ꯂꯣꯟ</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A5%A6_(%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE)" title="० (संख्या) – маратхі" lang="mr" hreflang="mr" data-title="० (संख्या)" data-language-autonym="मराठी" data-language-local-name="маратхі" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/0_(nombor)" title="0 (nombor) – малайская" lang="ms" hreflang="ms" data-title="0 (nombor)" data-language-autonym="Bahasa Melayu" data-language-local-name="малайская" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%81%80" title="၀ – бірманская" lang="my" hreflang="my" data-title="၀" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="бірманская" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%A7%D0%B0%D0%B2%D0%BE" title="Чаво – эрзянская" lang="myv" hreflang="myv" data-title="Чаво" data-language-autonym="Эрзянь" data-language-local-name="эрзянская" class="interlanguage-link-target">Эрзянь</a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%DB%B0" title="۰ – мазандэранская" lang="mzn" hreflang="mzn" data-title="۰" data-language-autonym="مازِرونی" data-language-local-name="мазандэранская" class="interlanguage-link-target">مازِرونی</a></li><li class="interlanguage-link interwiki-nap mw-list-item"><a href="https://nap.wikipedia.org/wiki/Zero" title="Zero – неапалітанская" lang="nap" hreflang="nap" data-title="Zero" data-language-autonym="Napulitano" data-language-local-name="неапалітанская" class="interlanguage-link-target">Napulitano</a></li><li class="interlanguage-link interwiki-nds-nl mw-list-item"><a href="https://nds-nl.wikipedia.org/wiki/0_(getal)" title="0 (getal) – ніжнесаксонская" lang="nds-NL" hreflang="nds-NL" data-title="0 (getal)" data-language-autonym="Nedersaksies" data-language-local-name="ніжнесаксонская" class="interlanguage-link-target">Nedersaksies</a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B6%E0%A5%82%E0%A4%A8%E0%A5%8D%E0%A4%AF" title="शून्य – неўары" lang="new" hreflang="new" data-title="शून्य" data-language-autonym="नेपाल भाषा" data-language-local-name="неўары" class="interlanguage-link-target">नेपाल भाषा</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/0_(getal)" title="0 (getal) – нідэрландская" lang="nl" hreflang="nl" data-title="0 (getal)" data-language-autonym="Nederlands" data-language-local-name="нідэрландская" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/0" title="0 – нарвежская (нюношк)" lang="nn" hreflang="nn" data-title="0" data-language-autonym="Norsk nynorsk" data-language-local-name="нарвежская (нюношк)" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/0_(tall)" title="0 (tall) – нарвежская (букмол)" lang="nb" hreflang="nb" data-title="0 (tall)" data-language-autonym="Norsk bokmål" data-language-local-name="нарвежская (букмол)" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Sero" title="Sero – Novial" lang="nov" hreflang="nov" data-title="Sero" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target">Novial</a></li><li class="interlanguage-link interwiki-nso mw-list-item"><a href="https://nso.wikipedia.org/wiki/0_(nomoro)" title="0 (nomoro) – паўночная сота" lang="nso" hreflang="nso" data-title="0 (nomoro)" data-language-autonym="Sesotho sa Leboa" data-language-local-name="паўночная сота" class="interlanguage-link-target">Sesotho sa Leboa</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/0_(nombre)" title="0 (nombre) – аксітанская" lang="oc" hreflang="oc" data-title="0 (nombre)" data-language-autonym="Occitan" data-language-local-name="аксітанская" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/0" title="0 – арома" lang="om" hreflang="om" data-title="0" data-language-autonym="Oromoo" data-language-local-name="арома" class="interlanguage-link-target">Oromoo</a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AD%A6_(%E0%AC%B8%E0%AC%82%E0%AC%96%E0%AD%8D%E0%AD%9F%E0%AC%BE)" title="୦ (ସଂଖ୍ୟା) – орыя" lang="or" hreflang="or" data-title="୦ (ସଂଖ୍ୟା)" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="орыя" class="interlanguage-link-target">ଓଡ଼ିଆ</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A8%BF%E0%A8%AB%E0%A8%BC%E0%A8%B0" title="ਸਿਫ਼ਰ – панджабі" lang="pa" hreflang="pa" data-title="ਸਿਫ਼ਰ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="панджабі" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/0" title="0 – польская" lang="pl" hreflang="pl" data-title="0" data-language-autonym="Polski" data-language-local-name="польская" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B5%D9%81%D8%B1" title="صفر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="صفر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%DB%B0" title="۰ – пушту" lang="ps" hreflang="ps" data-title="۰" data-language-autonym="پښتو" data-language-local-name="пушту" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/0_(n%C3%BAmero)" title="0 (número) – партугальская" lang="pt" hreflang="pt" data-title="0 (número)" data-language-autonym="Português" data-language-local-name="партугальская" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Ch%27usaq_yupay" title="Ch'usaq yupay – кечуа" lang="qu" hreflang="qu" data-title="Ch'usaq yupay" data-language-autonym="Runa Simi" data-language-local-name="кечуа" class="interlanguage-link-target">Runa Simi</a></li><li class="interlanguage-link interwiki-rn mw-list-item"><a href="https://rn.wikipedia.org/wiki/Ubusa" title="Ubusa – рундзі" lang="rn" hreflang="rn" data-title="Ubusa" data-language-autonym="Ikirundi" data-language-local-name="рундзі" class="interlanguage-link-target">Ikirundi</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/0_(cifr%C4%83)" title="0 (cifră) – румынская" lang="ro" hreflang="ro" data-title="0 (cifră)" data-language-autonym="Română" data-language-local-name="румынская" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9D%D0%BE%D0%BB%D1%8C" title="Ноль – руская" lang="ru" hreflang="ru" data-title="Ноль" data-language-autonym="Русский" data-language-local-name="руская" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/0_(%D1%87%D0%B8%D1%81%D0%BB%D0%BE)" title="0 (число) – Rusyn" lang="rue" hreflang="rue" data-title="0 (число)" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target">Русиньскый</a></li><li class="interlanguage-link interwiki-rw mw-list-item"><a href="https://rw.wikipedia.org/wiki/Ubusa" title="Ubusa – руанда" lang="rw" hreflang="rw" data-title="Ubusa" data-language-autonym="Ikinyarwanda" data-language-local-name="руанда" class="interlanguage-link-target">Ikinyarwanda</a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%B6%E0%A5%82%E0%A4%A8%E0%A5%8D%E0%A4%AF%E0%A4%AE%E0%A5%8D_(%E0%A4%B8%E0%A4%99%E0%A5%8D%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE)" title="शून्यम् (सङ्ख्या) – санскрыт" lang="sa" hreflang="sa" data-title="शून्यम् (सङ्ख्या)" data-language-autonym="संस्कृतम्" data-language-local-name="санскрыт" class="interlanguage-link-target">संस्कृतम्</a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9D%D1%83%D1%83%D0%BB" title="Нуул – якуцкая" lang="sah" hreflang="sah" data-title="Нуул" data-language-autonym="Саха тыла" data-language-local-name="якуцкая" class="interlanguage-link-target">Саха тыла</a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%90" title="᱐ – санталі" lang="sat" hreflang="sat" data-title="᱐" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="санталі" class="interlanguage-link-target">ᱥᱟᱱᱛᱟᱲᱤ</a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Zeru" title="Zeru – сіцылійская" lang="scn" hreflang="scn" data-title="Zeru" data-language-autonym="Sicilianu" data-language-local-name="сіцылійская" class="interlanguage-link-target">Sicilianu</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/0" title="0 – шатландская" lang="sco" hreflang="sco" data-title="0" data-language-autonym="Scots" data-language-local-name="шатландская" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/0_(broj)" title="0 (broj) – сербскахарвацкая" lang="sh" hreflang="sh" data-title="0 (broj)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="сербскахарвацкая" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/0_(am%E1%B8%8Dan)" title="0 (amḍan) – ташэльхіт" lang="shi" hreflang="shi" data-title="0 (amḍan)" data-language-autonym="Taclḥit" data-language-local-name="ташэльхіт" class="interlanguage-link-target">Taclḥit</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/0" title="0 – Simple English" lang="en-simple" hreflang="en-simple" data-title="0" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/0_(%C4%8D%C3%ADslo)" title="0 (číslo) – славацкая" lang="sk" hreflang="sk" data-title="0 (číslo)" data-language-autonym="Slovenčina" data-language-local-name="славацкая" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/0" title="0 – славенская" lang="sl" hreflang="sl" data-title="0" data-language-autonym="Slovenščina" data-language-local-name="славенская" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Chipasina" title="Chipasina – шона" lang="sn" hreflang="sn" data-title="Chipasina" data-language-autonym="ChiShona" data-language-local-name="шона" class="interlanguage-link-target">ChiShona</a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/0_(tiro)" title="0 (tiro) – самалі" lang="so" hreflang="so" data-title="0 (tiro)" data-language-autonym="Soomaaliga" data-language-local-name="самалі" class="interlanguage-link-target">Soomaaliga</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/0_(num%C3%ABr)" title="0 (numër) – албанская" lang="sq" hreflang="sq" data-title="0 (numër)" data-language-autonym="Shqip" data-language-local-name="албанская" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/0_(%D0%B1%D1%80%D0%BE%D1%98)" title="0 (број) – сербская" lang="sr" hreflang="sr" data-title="0 (број)" data-language-autonym="Српски / srpski" data-language-local-name="сербская" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-srn mw-list-item"><a href="https://srn.wikipedia.org/wiki/Numro_0" title="Numro 0 – сранан-тонга" lang="srn" hreflang="srn" data-title="Numro 0" data-language-autonym="Sranantongo" data-language-local-name="сранан-тонга" class="interlanguage-link-target">Sranantongo</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/0_(tal)" title="0 (tal) – шведская" lang="sv" hreflang="sv" data-title="0 (tal)" data-language-autonym="Svenska" data-language-local-name="шведская" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Sifuri" title="Sifuri – суахілі" lang="sw" hreflang="sw" data-title="Sifuri" data-language-autonym="Kiswahili" data-language-local-name="суахілі" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/0" title="0 – Silesian" lang="szl" hreflang="szl" data-title="0" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target">Ślůnski</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/0_(%E0%AE%8E%E0%AE%A3%E0%AF%8D)" title="0 (எண்) – тамільская" lang="ta" hreflang="ta" data-title="0 (எண்)" data-language-autonym="தமிழ்" data-language-local-name="тамільская" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B1%81%E0%B0%A8%E0%B1%8D%E0%B0%A8" title="సున్న – тэлугу" lang="te" hreflang="te" data-title="సున్న" data-language-autonym="తెలుగు" data-language-local-name="тэлугу" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A1%D0%B8%D1%84%D1%80" title="Сифр – таджыкская" lang="tg" hreflang="tg" data-title="Сифр" data-language-autonym="Тоҷикӣ" data-language-local-name="таджыкская" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/0" title="0 – тайская" lang="th" hreflang="th" data-title="0" data-language-autonym="ไทย" data-language-local-name="тайская" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/0_(bilang)" title="0 (bilang) – Tagalog" lang="tl" hreflang="tl" data-title="0 (bilang)" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/0" title="0 – турэцкая" lang="tr" hreflang="tr" data-title="0" data-language-autonym="Türkçe" data-language-local-name="турэцкая" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Tandza" title="Tandza – тсонга" lang="ts" hreflang="ts" data-title="Tandza" data-language-autonym="Xitsonga" data-language-local-name="тсонга" class="interlanguage-link-target">Xitsonga</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/0_(%D1%81%D0%B0%D0%BD)" title="0 (сан) – татарская" lang="tt" hreflang="tt" data-title="0 (сан)" data-language-autonym="Татарча / tatarça" data-language-local-name="татарская" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/0_(%D1%87%D0%B8%D1%81%D0%BB%D0%BE)" title="0 (число) – украінская" lang="uk" hreflang="uk" data-title="0 (число)" data-language-autonym="Українська" data-language-local-name="украінская" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B5%D9%81%D8%B1_(%D8%B9%D8%AF%D8%AF)" title="صفر (عدد) – урду" lang="ur" hreflang="ur" data-title="صفر (عدد)" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/0_(son)" title="0 (son) – узбекская" lang="uz" hreflang="uz" data-title="0 (son)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбекская" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/0_(lugu)" title="0 (lugu) – Veps" lang="vep" hreflang="vep" data-title="0 (lugu)" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target">Vepsän kel’</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/0_(s%E1%BB%91)" title="0 (số) – в’етнамская" lang="vi" hreflang="vi" data-title="0 (số)" data-language-autonym="Tiếng Việt" data-language-local-name="в’етнамская" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/0_(getal)" title="0 (getal) – West Flemish" lang="vls" hreflang="vls" data-title="0 (getal)" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target">West-Vlams</a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/0" title="0 – валонская" lang="wa" hreflang="wa" data-title="0" data-language-autonym="Walon" data-language-local-name="валонская" class="interlanguage-link-target">Walon</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/0_(ihap)" title="0 (ihap) – варай" lang="war" hreflang="war" data-title="0 (ihap)" data-language-autonym="Winaray" data-language-local-name="варай" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Tus" title="Tus – валоф" lang="wo" hreflang="wo" data-title="Tus" data-language-autonym="Wolof" data-language-local-name="валоф" class="interlanguage-link-target">Wolof</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/0" title="0 – ву" lang="wuu" hreflang="wuu" data-title="0" data-language-autonym="吴语" data-language-local-name="ву" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/0" title="0 – калмыцкая" lang="xal" hreflang="xal" data-title="0" data-language-autonym="Хальмг" data-language-local-name="калмыцкая" class="interlanguage-link-target">Хальмг</a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/Iqanda" title="Iqanda – коса" lang="xh" hreflang="xh" data-title="Iqanda" data-language-autonym="IsiXhosa" data-language-local-name="коса" class="interlanguage-link-target">IsiXhosa</a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%9C%E1%83%A3%E1%83%9A%E1%83%98" title="ნული – Mingrelian" lang="xmf" hreflang="xmf" data-title="ნული" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target">მარგალური</a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/0_(%D7%A0%D7%95%D7%9E%D7%A2%D7%A8)" title="0 (נומער) – ідыш" lang="yi" hreflang="yi" data-title="0 (נומער)" data-language-autonym="ייִדיש" data-language-local-name="ідыш" class="interlanguage-link-target">ייִדיש</a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/0_(n%E1%BB%8D%CC%81mb%C3%A0)" title="0 (nọ́mbà) – ёруба" lang="yo" hreflang="yo" data-title="0 (nọ́mbà)" data-language-autonym="Yorùbá" data-language-local-name="ёруба" class="interlanguage-link-target">Yorùbá</a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/0_(%E2%B4%B0%E2%B5%8E%E2%B4%B9%E2%B4%B0%E2%B5%8F)" title="0 (ⴰⵎⴹⴰⵏ) – стандартная мараканская тамазіхт" lang="zgh" hreflang="zgh" data-title="0 (ⴰⵎⴹⴰⵏ)" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="стандартная мараканская тамазіхт" class="interlanguage-link-target">ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/0" title="0 – кітайская" lang="zh" hreflang="zh" data-title="0" data-language-autonym="中文" data-language-local-name="кітайская" class="interlanguage-link-target">中文</a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E3%80%87" title="〇 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="〇" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target">文言</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/0" title="0 – Minnan" lang="nan" hreflang="nan" data-title="0" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/0" title="0 – кантонскі дыялект кітайскай" lang="yue" hreflang="yue" data-title="0" data-language-autonym="粵語" data-language-local-name="кантонскі дыялект кітайскай" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Iqanda(inombolo)" title="Iqanda(inombolo) – зулу" lang="zu" hreflang="zu" data-title="Iqanda(inombolo)" data-language-autonym="IsiZulu" data-language-local-name="зулу" class="interlanguage-link-target">IsiZulu</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q204#sitelinks-wikipedia" title="Правіць міжмоўныя спасылкі" class="wbc-editpage">Правіць спасылкі</a></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/0_(%D0%BB%D1%96%D0%BA)" title="Паказаць уласна змест старонкі [c]" accesskey="c">Старонка</a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%D0%A0%D0%B0%D0%B7%D0%BC%D0%BE%D0%B2%D1%8B:0_(%D0%BB%D1%96%D0%BA)" rel="discussion" title="Размовы пра змест гэтай старонкі [t]" accesskey="t">Размовы</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="Змяніць моўны варыянт" > <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" >беларуская </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="Віды"> <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/0_(%D0%BB%D1%96%D0%BA)">Чытаць</a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit" title="Правіць старонку [v]" accesskey="v">Правіць</a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit" title="Правіць зыходны код гэтай старонкі [e]" accesskey="e">Правіць зыходнік</a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=history" title="Ранейшыя версіі гэтай старонкі. [h]" accesskey="h">Паказаць гісторыю</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="Інструменты" > <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" >Інструменты </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">Інструменты</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">перанесці да бакавой панэлі</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="Больш магчымасцей" > <div class="vector-menu-heading"> Дзеянні </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/0_(%D0%BB%D1%96%D0%BA)">Чытаць</a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit" title="Правіць старонку [v]" accesskey="v">Правіць</a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit" title="Правіць зыходны код гэтай старонкі [e]" accesskey="e">Правіць зыходнік</a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=history">Паказаць гісторыю</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%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:WhatLinksHere/0_(%D0%BB%D1%96%D0%BA)" title="Спіс вікістаронак, якія спасылаюцца сюды [j]" accesskey="j">Сюды спасылаюцца</a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:RecentChangesLinked/0_(%D0%BB%D1%96%D0%BA)" rel="nofollow" title="Нядаўнія змены ў старонках, на якія спасылаецца гэтая старонка [k]" accesskey="k">Звязаныя праўкі</a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:SpecialPages" title="Пералік усіх адмысловых старонак [q]" accesskey="q">Адмысловыя старонкі</a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&oldid=4735370" title="Нязменная спасылка на гэтую версію гэтай старонкі">Нязменная спасылка</a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=info" title="Больш звестак пра гэту старонку">Звесткі пра старонку</a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:CiteThisPage&page=0_%28%D0%BB%D1%96%D0%BA%29&id=4735370&wpFormIdentifier=titleform" title="Інфармацыя пра тое, як цытаваць гэтую старонку">Цытаваць гэту старонку</a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:UrlShortener&url=https%3A%2F%2Fbe.wikipedia.org%2Fwiki%2F0_%28%25D0%25BB%25D1%2596%25D0%25BA%29">Атрымаць скарочаны URL-адрас</a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:QrCode&url=https%3A%2F%2Fbe.wikipedia.org%2Fwiki%2F0_%28%25D0%25BB%25D1%2596%25D0%25BA%29">Спампаваць QR-код</a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Друк/экспарт </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:Book&bookcmd=book_creator&referer=0+%28%D0%BB%D1%96%D0%BA%29">Стварыць кнігу</a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:DownloadAsPdf&page=0_%28%D0%BB%D1%96%D0%BA%29&action=show-download-screen">Спампаваць як PDF</a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&printable=yes" title="Друкавальная версія гэтай старонкі [p]" accesskey="p">Для друку</a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> У іншых праектах </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:0_(number)" hreflang="en">Вікісховішча</a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q204" title="Спасылка на звязаны элемент рэпазітара даных [g]" accesskey="g">Элемент Вікіданых</a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Выгляд"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Выгляд</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">перанесці да бакавой панэлі</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">З Вікіпедыі, свабоднай энцыклапедыі</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" dir="ltr">0 (нуль ад <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">лац.</a>: nullus — ніякі) — <a href="/wiki/%D0%A6%D1%8D%D0%BB%D1%8B_%D0%BB%D1%96%D0%BA" title="Цэлы лік">цэлы лік</a>, які раздзяляе на <a href="/wiki/%D0%9B%D1%96%D0%BA%D0%B0%D0%B2%D0%B0%D1%8F_%D0%B2%D0%BE%D1%81%D1%8C" class="mw-redirect" title="Лікавая вось">лікавай прамой</a> <a href="/wiki/%D0%94%D0%B0%D0%B4%D0%B0%D1%82%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Дадатны лік">дадатныя</a> і <a href="/wiki/%D0%90%D0%B4%D0%BC%D0%BE%D1%9E%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Адмоўны лік">адмоўныя</a> лікі. Выконвае цэнтральную роль у матэматыцы як элемент, <a href="/w/index.php?title=%D0%9D%D0%B5%D0%B9%D1%82%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82&action=edit&redlink=1" class="new" title="Нейтральны элемент (няма такой старонкі)">нейтральны</a><a href="https://en.wikipedia.org/wiki/Identity_element" class="extiw" title="en:Identity element">[en]</a> адносна <a href="/wiki/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%B0%D0%BD%D0%BD%D0%B5" title="Складанне">складання</a> цэлых, <a href="/wiki/%D0%A0%D1%8D%D1%87%D0%B0%D1%96%D1%81%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Рэчаісны лік">рэчаісных лікаў</a>, і іншых <a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D1%96%D1%87%D0%BD%D0%B0%D1%8F_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Алгебраічная структура (няма такой старонкі)">алгебраічных структур</a><a href="https://en.wikipedia.org/wiki/Algebraic_structure" class="extiw" title="en:Algebraic structure">[en]</a>. У <a href="/w/index.php?title=%D0%9F%D0%B0%D0%B7%D1%96%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D1%8F_%D0%BD%D0%B0%D1%82%D0%B0%D1%86%D1%8B%D1%8F&action=edit&redlink=1" class="new" title="Пазіцыйная натацыя (няма такой старонкі)">пазіцыйнай натацыі</a><a href="https://en.wikipedia.org/wiki/Positional_notation" class="extiw" title="en:Positional notation">[en]</a>, напрыклад <a href="/wiki/%D0%94%D0%B7%D0%B5%D1%81%D1%8F%D1%82%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Дзесятковая сістэма злічэння">дзесятковай</a>, нуль выступае яшчэ і як <a href="/wiki/%D0%9B%D1%96%D1%87%D0%B1%D0%B0" title="Лічба">лічба</a> для пазначэння таго, што адпаведная ступень 10 не дамнажаецца ні на што і не дадаецца да выніку. Здаецца, што гістарычна такую канцэпцыю было цяжка прыдумаць. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Асноўныя_ўласцівасці_нуля">Асноўныя ўласцівасці нуля</h2>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=1" title="Правіць раздзел: Асноўныя ўласцівасці нуля" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=1" title="Правіць зыходнік раздзела: Асноўныя ўласцівасці нуля">правіць зыходнік</a>]</div> <ul><li>Нуль не мае <a href="/wiki/%D0%97%D0%BD%D0%B0%D0%BA" title="Знак">знака</a>.</li> <li>Любы <a href="/wiki/%D0%9B%D1%96%D0%BA" title="Лік">лік</a> пры <a href="/wiki/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%B0%D0%BD%D0%BD%D0%B5" title="Складанне">складанні</a> з нулём не мяняецца.</li> <li>Пры <a href="/wiki/%D0%90%D0%B4%D0%BD%D1%96%D0%BC%D0%B0%D0%BD%D0%BD%D0%B5" title="Адніманне">адніманні</a> нуля з любога ліку атрымліваецца той жа лік.</li> <li><a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B0%D0%BD%D0%BD%D0%B5" title="Множанне">Дамнажэнне</a> любога ліку на нуль дае нуль.</li> <li>Пры <a href="/wiki/%D0%94%D0%B7%D1%8F%D0%BB%D0%B5%D0%BD%D0%BD%D0%B5" title="Дзяленне">дзяленні</a> нуля на любы лік, акрамя самога 0, атрымліваецца нуль. Дзяленне нуля на нуль прыводзіць да <a href="/w/index.php?title=%D0%A0%D0%B0%D1%81%D0%BA%D1%80%D1%8B%D1%86%D1%86%D1%91_%D0%BD%D1%8F%D0%B2%D1%8B%D0%B7%D0%BD%D0%B0%D1%87%D0%B0%D0%BD%D0%B0%D1%81%D1%86%D0%B5%D0%B9&action=edit&redlink=1" class="new" title="Раскрыццё нявызначанасцей (няма такой старонкі)">нявызначанасці</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (0/0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (0/0)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a64f835b22bba1e49b1e05ba2d971c7d15fc2df8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.297ex; height:2.843ex;" alt="{\displaystyle (0/0)}">.</li> <li>Нуль з’яўляецца <a href="/w/index.php?title=%D0%A6%D0%BE%D1%82%D0%BD%D1%8B%D1%8F_%D1%96_%D0%BD%D1%8F%D1%86%D0%BE%D1%82%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Цотныя і няцотныя лікі (няма такой старонкі)">цотным</a> лікам, бо пры дзяленні на 2 атрымліваецца <a href="/wiki/%D0%A6%D1%8D%D0%BB%D1%8B_%D0%BB%D1%96%D0%BA" title="Цэлы лік">цэлы лік</a>.</li> <li><a href="/w/index.php?title=%D0%94%D0%B7%D1%8F%D0%BB%D0%B5%D0%BD%D0%BD%D0%B5_%D0%BD%D0%B0_%D0%BD%D1%83%D0%BB%D1%8C&action=edit&redlink=1" class="new" title="Дзяленне на нуль (няма такой старонкі)">Дзяленне на нуль</a> немагчыма ў прасторы камплексных лікаў. На самай справе, калі абазначыць <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {a}{0}}=b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mn>0</mn> </mfrac> </mrow> <mo>=</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a}{0}}=b}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ae9720eae9eb9086fae770d1a1dd093e9b4e196" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.162ex; height:4.676ex;" alt="{\displaystyle {\frac {a}{0}}=b}">, то па азначэнні дзялення фармальна павінна быць <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b\cdot 0=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>⋅</mo> <mn>0</mn> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\cdot 0=a}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/485f13c1fd84eb6519cd6c904f7362d0e7d1d3b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.167ex; height:2.176ex;" alt="{\displaystyle b\cdot 0=a}">, у той час як выраз <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b\cdot 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>⋅</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\cdot 0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47ca2ab9a00ba0cadb5a934ea585a706e511d926" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.839ex; height:2.176ex;" alt="{\displaystyle b\cdot 0}">, пры любым камплексным <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><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}">, ровен нулю. Іншымі словамі, для нуля не існуе <a href="/w/index.php?title=%D0%90%D0%B4%D0%B2%D0%B0%D1%80%D0%BE%D1%82%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&redlink=1" class="new" title="Адваротны лік (няма такой старонкі)">адваротнага ліку</a> ў прасторы комплексных лікаў. Але гэта магчыма на <a href="/wiki/%D0%9A%D0%B0%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%B0%D1%8F_%D0%BF%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C#Бесканечна_аддалены_пункт" title="Камплексная плоскасць">пашыранай камплекснай плоскасці</a>.</li> <li>Пры ўзвядзенні любога ліку, акрамя нуля, ў нулявую ступень па азначэнні атрымліваецца 1: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n^{0}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n^{0}=1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0e18cad3fbc3bd7cbf9f42ac0f07c381d3e8d94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.71ex; height:2.676ex;" alt="{\displaystyle n^{0}=1}">, пры <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\neq 0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5920e98ff3dd1cb41e01f76243300450c958d5e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.656ex; height:2.676ex;" alt="{\displaystyle n\neq 0}">.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Абагульненні">Абагульненні</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=2" title="Правіць раздзел: Абагульненні" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=2" title="Правіць зыходнік раздзела: Абагульненні">правіць зыходнік</a>]</div> Аналаг нуля можна ўвесці ў любым мностве, на якім вызначана аперацыя складання; у <a href="/wiki/%D0%90%D0%B1%D1%81%D1%82%D1%80%D0%B0%D0%BA%D1%82%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Абстрактная алгебра">вышэйшай алгебры</a> такі элемент называецца <a href="/w/index.php?title=%D0%9D%D0%B5%D0%B9%D1%82%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82&action=edit&redlink=1" class="new" title="Нейтральны элемент (няма такой старонкі)">нейтральным элементам</a> (або, у залежнасці ад умоўнай назвы групавой аперацыі, адытыўным нулём, ці мультыплікатыўнай адзінкай). Часцей за ўсё выкарыстоўваецца <a href="/wiki/%D0%A0%D1%8D%D1%87%D0%B0%D1%96%D1%81%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Рэчаісны лік">рэчаісны</a> нуль, г.зн. нуль у кантэксце мноства <a href="/wiki/%D0%A0%D1%8D%D1%87%D0%B0%D1%96%D1%81%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96" class="mw-redirect" title="Рэчаісныя лікі">рэчаісных лікаў</a>. Іншыя распаўсюджаныя варыяцыі: <ul><li><a href="/wiki/%D0%9D%D1%83%D0%BB%D1%8F%D0%B2%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%80%D1%8B%D1%86%D0%B0" title="Нулявая матрыца">Нулявая матрыца</a></li> <li><a href="/wiki/%D0%9D%D1%83%D0%BB%D1%8F%D0%B2%D1%8B_%D0%B2%D0%B5%D0%BA%D1%82%D0%B0%D1%80" title="Нулявы вектар">Нуль-вектар</a></li> <li><a href="/wiki/%D0%9F%D1%83%D0%BD%D0%BA%D1%82" title="Пункт">Пункт</a> (як <a href="/wiki/%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%BD%D0%B0%D1%81%D1%86%D1%8C_%D0%BF%D1%80%D0%B0%D1%81%D1%82%D0%BE%D1%80%D1%8B" title="Размернасць прасторы">нульмерны аб'ект</a>, ці нульмерная прастора)</li> <li>Нулявы <a href="/wiki/%D0%9C%D0%BD%D0%B0%D0%B3%D0%B0%D1%87%D0%BB%D0%B5%D0%BD" title="Мнагачлен">мнагачлен</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Адносіны_да_натуральных_лікаў">Адносіны да натуральных лікаў</h2>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=3" title="Правіць раздзел: Адносіны да натуральных лікаў" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=3" title="Правіць зыходнік раздзела: Адносіны да натуральных лікаў">правіць зыходнік</a>]</div> Існуюць два падыходы да вызначэння <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="Натуральны лік">натуральных лікаў</a> — адны аўтары адносяць нуль да натуральных лікаў<a href="#cite_note-1">[1]</a>, іншыя — не. У краінах былога СССР (у тым ліку, і Беларусі) у школьных праграмах па матэматыцы не прынята адносіць нуль да натуральных лікаў (бо натуральнымі лікамі там азначаюцца як лікі, якія выкарыстоўваюцца пры лічэнні, а 0 пры лічэнні не выкарыстоўваецца), хоць гэта абцяжарвае некаторыя фармулёўкі (напрыклад, прыходзіцца адрозніваць дзяленне з астачай і дзяленне без астачы). <div class="mw-heading mw-heading2"><h2 id="Ужыванне">Ужыванне</h2>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=4" title="Правіць раздзел: Ужыванне" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=4" title="Правіць зыходнік раздзела: Ужыванне">правіць зыходнік</a>]</div> <div class="mw-heading mw-heading3"><h3 id="У_матэматыцы">У матэматыцы</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=5" title="Правіць раздзел: У матэматыцы" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=5" title="Правіць зыходнік раздзела: У матэматыцы">правіць зыходнік</a>]</div> <ul><li>Нулявы <a href="/wiki/%D0%9B%D1%96%D0%BA%D1%96_%D0%A4%D1%96%D0%B1%D0%B0%D0%BD%D0%B0%D1%87%D1%8B" title="Лікі Фібаначы">лік Фібаначы</a>, нулявы <a href="/w/index.php?title=%D0%9B%D1%96%D0%BA_%D0%9C%D0%B5%D1%80%D1%81%D0%B5%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Лік Мерсена (няма такой старонкі)">лік Мерсена</a>, нулявы <a href="/w/index.php?title=%D0%A2%D1%80%D0%BE%D1%85%D0%B2%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&redlink=1" class="new" title="Трохвугольны лік (няма такой старонкі)">трохвугольны лік</a> і г. д.</li> <li>0<a href="/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%B0%D1%80%D1%8B%D1%8F%D0%BB" title="Фактарыял">!</a> (Нуль <a href="/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%B0%D1%80%D1%8B%D1%8F%D0%BB" title="Фактарыял">фактарыял</a>) вызначаецца як 1.</li> <li>Становішчы 0 і <a href="/w/index.php?title=360,_%D0%BB%D1%96%D0%BA&action=edit&redlink=1" class="new" title="360, лік (няма такой старонкі)">360</a> <a href="/w/index.php?title=%D0%93%D1%80%D0%B0%D0%B4%D1%83%D1%81,_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F&action=edit&redlink=1" class="new" title="Градус, геаметрыя (няма такой старонкі)">градусаў</a> супадаюць</li> <li><a href="/wiki/%D0%9D%D1%83%D0%BB%D1%8C_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%96" title="Нуль функцыі">Нуль функцыі</a></li></ul> <dl><dt>Нявызначанасці з удзелам нуля</dt></dl> У <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Матэматычны аналіз">матэматычным аналізе</a> магчыма 7 <a href="/w/index.php?title=%D0%A0%D0%B0%D1%81%D0%BA%D1%80%D1%8B%D1%86%D1%86%D1%91_%D0%BD%D1%8F%D0%B2%D1%8B%D0%B7%D0%BD%D0%B0%D1%87%D0%B0%D0%BD%D0%B0%D1%81%D1%86%D0%B5%D0%B9&action=edit&redlink=1" class="new" title="Раскрыццё нявызначанасцей (няма такой старонкі)">нявызначаных сітуацый</a>, у 4 з якіх фармальна прысутнічае нуль (ён абазначае <a href="/w/index.php?title=%D0%90%D0%BD%D0%B0%D0%BB%D1%96%D0%B7_%D0%B1%D0%B5%D1%81%D0%BA%D0%B0%D0%BD%D0%B5%D1%87%D0%BD%D0%B0_%D0%BC%D0%B0%D0%BB%D1%8B%D1%85&action=edit&redlink=1" class="new" title="Аналіз бесканечна малых (няма такой старонкі)">бесканечна малую велічыню</a>): <center> <table class="wikitable"> <tbody><tr align="center"> <td width="70"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {0}{0}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0</mn> <mn>0</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {0}{0}}\right)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd755a1402cbe1293ddb34085a64afa3e6e6a94e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:5.42ex; height:6.176ex;" alt="{\displaystyle \left({\frac {0}{0}}\right)}"> </td> <td width="70"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (0^{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (0^{0})}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc9f485b1dbb57bb5ff274ef7c635e795fd4003b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.026ex; height:3.176ex;" alt="{\displaystyle (0^{0})}"> </td> <td width="70"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\infty ^{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi mathvariant="normal">∞</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\infty ^{0})}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9d8167e0ddb6edfcf9e6b96ac3a50fdb45a8816" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.187ex; height:3.176ex;" alt="{\displaystyle (\infty ^{0})}"> </td> <td width="70"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (0\cdot \infty )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>0</mn> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (0\cdot \infty )}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36788c7ed8e66e2e2312530eac81bb2ef7f703cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.975ex; height:2.843ex;" alt="{\displaystyle (0\cdot \infty )}"> </td></tr></tbody></table> </center> І цалкам вызначаная сітуацыя, калі разглядаецца граніца бесканечна малой велічыні (<a href="/w/index.php?title=%D0%90%D0%B4%D0%BD%D0%B0%D0%B1%D0%B0%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D0%B3%D1%80%D0%B0%D0%BD%D1%96%D1%86%D0%B0&action=edit&redlink=1" class="new" title="Аднабаковая граніца (няма такой старонкі)">справа ці злева</a>): <dl><dd><ul><li>Правая граніца: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{x\to 0+0}{\frac {1}{x}}=\left({\frac {1}{0}}\right)=+\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> <mo>+</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>0</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to 0+0}{\frac {1}{x}}=\left({\frac {1}{0}}\right)=+\infty }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f53ff771f12f13fb4b2825488ed7b5b790ea2bca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.807ex; height:6.176ex;" alt="{\displaystyle \lim _{x\to 0+0}{\frac {1}{x}}=\left({\frac {1}{0}}\right)=+\infty }">   ці   <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{x}}\right){\xrightarrow[{x{\xrightarrow {}}0+0}]{}}+\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em" /> </mover> </mrow> <mn>0</mn> <mo>+</mo> <mn>0</mn> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em" /> </munderover> </mrow> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{x}}\right){\xrightarrow[{x{\xrightarrow {}}0+0}]{}}+\infty }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fd77782d299adcb0db058db1562513911932085" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.208ex; margin-bottom: -0.464ex; width:17.968ex; height:6.343ex;" alt="{\displaystyle \left({\frac {1}{x}}\right){\xrightarrow[{x{\xrightarrow {}}0+0}]{}}+\infty }"></li> <li>Левая граніца: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{x\to 0-0}{\frac {1}{x}}=\left({\frac {1}{0}}\right)=-\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> <mo>−</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>0</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to 0-0}{\frac {1}{x}}=\left({\frac {1}{0}}\right)=-\infty }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8374df83dd18bc117dfe06ab92c308c5b6817799" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.807ex; height:6.176ex;" alt="{\displaystyle \lim _{x\to 0-0}{\frac {1}{x}}=\left({\frac {1}{0}}\right)=-\infty }">   ці   <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{x}}\right){\xrightarrow[{x{\xrightarrow {}}0-0}]{}}-\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em" /> </mover> </mrow> <mn>0</mn> <mo>−</mo> <mn>0</mn> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em" /> </munderover> </mrow> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{x}}\right){\xrightarrow[{x{\xrightarrow {}}0-0}]{}}-\infty }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03a3e874d165a4ed6922c75464d4f4451bd20d44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.208ex; margin-bottom: -0.464ex; width:17.968ex; height:6.343ex;" alt="{\displaystyle \left({\frac {1}{x}}\right){\xrightarrow[{x{\xrightarrow {}}0-0}]{}}-\infty }"></li></ul></dd></dl> <div class="mw-heading mw-heading3"><h3 id="У_фізіцы">У фізіцы</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=6" title="Правіць раздзел: У фізіцы" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=6" title="Правіць зыходнік раздзела: У фізіцы">правіць зыходнік</a>]</div> <ul><li><a href="/wiki/%D0%90%D0%B1%D1%81%D0%B0%D0%BB%D1%8E%D1%82%D0%BD%D1%8B_%D0%BD%D1%83%D0%BB%D1%8C_%D1%82%D1%8D%D0%BC%D0%BF%D0%B5%D1%80%D0%B0%D1%82%D1%83%D1%80%D1%8B" title="Абсалютны нуль тэмпературы">Абсалютны нуль тэмпературы</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="У_іншых_галінах">У іншых галінах</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=7" title="Правіць раздзел: У іншых галінах" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=7" title="Правіць зыходнік раздзела: У іншых галінах">правіць зыходнік</a>]</div> <ul><li><a href="/wiki/ASCII" title="ASCII">ASCII</a> — код кіруючага сімвала <code>NULL</code>.</li> <li><a href="/wiki/0_%D0%B3%D0%BE%D0%B4" class="mw-redirect" title="0 год">Нулявога года</a> ў <a href="/wiki/%D0%AE%D0%BB%D1%96%D1%8F%D0%BD%D1%81%D0%BA%D1%96_%D0%BA%D0%B0%D0%BB%D1%8F%D0%BD%D0%B4%D0%B0%D1%80" title="Юліянскі каляндар">юліянскім</a> і <a href="/wiki/%D0%93%D1%80%D1%8B%D0%B3%D0%B0%D1%80%D1%8B%D1%8F%D0%BD%D1%81%D0%BA%D1%96_%D0%BA%D0%B0%D0%BB%D1%8F%D0%BD%D0%B4%D0%B0%D1%80" title="Грыгарыянскі каляндар">Грыгарыянскім</a> календары няма, гэтак жа, як няма нулявога дня ў годзе і нулявога дня ў месяцы. Аднак існуе <a href="https://en.wikipedia.org/wiki/Astronomical_year_numbering" class="extiw" title="en:Astronomical year numbering">астранамічнае летазлічэнне</a><a href="/w/index.php?title=%D0%90%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B0%D0%BC%D1%96%D1%87%D0%BD%D0%B0%D0%B5_%D0%BB%D0%B5%D1%82%D0%B0%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D0%B5&action=edit&redlink=1" class="new" title="Астранамічнае летазлічэнне (няма такой старонкі)">be</a>en, у якім <a href="/wiki/0_%D0%B3%D0%BE%D0%B4" class="mw-redirect" title="0 год">нулявы</a> год ёсць.</li> <li><a href="/w/index.php?title=%D0%9D%D1%83%D0%BB%D1%8F%D0%B2%D1%8B_%D0%BA%D1%96%D0%BB%D0%B0%D0%BC%D0%B5%D1%82%D1%80&action=edit&redlink=1" class="new" title="Нулявы кіламетр (няма такой старонкі)">Нулявы кіламетр</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Гісторыя">Гісторыя</h2>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=8" title="Правіць раздзел: Гісторыя" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=8" title="Правіць зыходнік раздзела: Гісторыя">правіць зыходнік</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Старажытны_Блізкі_Усход">Старажытны Блізкі Усход</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=9" title="Правіць раздзел: Старажытны Блізкі Усход" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=9" title="Правіць зыходнік раздзела: Старажытны Блізкі Усход">правіць зыходнік</a>]</div> <table style="float:right; clear:right; text-align:center; border: 1px solid; margin: 8px" align="right" cellspacing="0" cellpadding="8"> <tbody><tr> <th>нефер   </th> <td>сэрца з <a href="/wiki/%D0%A2%D1%80%D0%B0%D1%85%D0%B5%D1%8F" title="Трахея">трахеяй</a> прыгожы, прыемны, добры </td> <td><table class="mw-hiero-table mw-hiero-outer" dir="ltr"><tbody><tr><td> <table class="mw-hiero-table"><tbody><tr> <td><img class="skin-invert" style="margin: 1px;" src="/w/extensions/wikihiero/img/hiero_F35.png?9f378" height="38" title="F35" alt="F35" /></td></tr></tbody></table> </td></tr></tbody></table> </td></tr></tbody></table> Старажытныя <a href="/wiki/%D0%95%D0%B3%D1%96%D0%BF%D0%B5%D1%86%D0%BA%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Егіпецкая сістэма злічэння">егіпецкія лічбы</a> былі <a href="/wiki/%D0%94%D0%B7%D0%B5%D1%81%D1%8F%D1%82%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Дзесятковая сістэма злічэння">дзесятковымі</a><a href="#cite_note-2">[2]</a>. <a href="/wiki/%D0%95%D0%B3%D1%96%D0%BF%D0%B5%D1%86%D0%BA%D1%96%D1%8F_%D1%96%D0%B5%D1%80%D0%BE%D0%B3%D0%BB%D1%96%D1%84%D1%8B" title="Егіпецкія іерогліфы">Іерогліфы</a> выкарыстоўваліся ў якасці лічбаў у <a href="/w/index.php?title=%D0%9D%D0%B5%D0%BF%D0%B0%D0%B7%D1%96%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D1%8F_%D0%BD%D0%B0%D1%82%D0%B0%D1%86%D1%8B%D1%8F&action=edit&redlink=1" class="new" title="Непазіцыйная натацыя (няма такой старонкі)">непазіцыйнай натацыі</a><a href="https://en.wikipedia.org/wiki/Sign-value_notation" class="extiw" title="en:Sign-value notation">[en]</a>. К 1770 г. да н.э. у егіпцян з’явіўся сімвал нуля ў гаспадарчых тэкстах. Сімвал <a href="/w/index.php?title=%D0%9D%D0%B5%D1%84%D0%B5%D1%80&action=edit&redlink=1" class="new" title="Нефер (няма такой старонкі)">нефер</a><a href="https://en.wikipedia.org/wiki/Nefer" class="extiw" title="en:Nefer">[en]</a>, што значыць прыгожы, выкарыстоўвалі яшчэ і для абазначэння базавага ўзроўню на малюнках магільняў і пірамід, ад якога адмяраліся ўсе адлегласці зверху і знізу<a href="#cite_note-3">[3]</a>. К сярэдзіне <a href="/wiki/2_%D1%82%D1%8B%D1%81%D1%8F%D1%87%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5_%D0%B4%D0%B0_%D0%BD.%D1%8D." title="2 тысячагоддзе да н.э.">2-га тысячагоддзя да н.э.</a> <a href="/w/index.php?title=%D0%92%D0%B0%D0%B2%D1%96%D0%BB%D0%BE%D0%BD%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0&action=edit&redlink=1" class="new" title="Вавілонская матэматыка (няма такой старонкі)">вавілонская матэматыка</a><a href="https://en.wikipedia.org/wiki/Babylonian_mathematics" class="extiw" title="en:Babylonian mathematics">[en]</a> мела складаную <a href="/w/index.php?title=%D0%A8%D0%B0%D1%81%D1%86%D1%96%D0%B4%D0%B7%D0%B5%D1%81%D1%8F%D1%82%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F&action=edit&redlink=1" class="new" title="Шасцідзесятковая сістэма злічэння (няма такой старонкі)">шасцідзесятковую</a><a href="https://en.wikipedia.org/wiki/Sexagesimal" class="extiw" title="en:Sexagesimal">[en]</a> сістэму злічэння. Адсутнасць пазіцыйнага значэння пазначалася прабелам паміж шасцідзесятковымі лічбамі. На таблічцы, раскапанай у <a href="/wiki/%D0%9A%D1%96%D1%88_(%D0%A8%D1%83%D0%BC%D0%B5%D1%80)" title="Кіш (Шумер)">Кішы</a> (якая датуецца яшчэ 700 г. да н. э.), перапісчык Бел-бан-аплу выкарыстаў тры кручкі замест прабелу ў той жа <a href="/w/index.php?title=%D0%92%D0%B0%D0%B2%D1%96%D0%BB%D0%BE%D0%BD%D1%81%D0%BA%D1%96%D1%8F_%D0%BB%D1%96%D1%87%D0%B1%D1%8B&action=edit&redlink=1" class="new" title="Вавілонскія лічбы (няма такой старонкі)">вавілонскай сістэме</a><a href="https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals" class="extiw" title="en:Babylonian cuneiform numerals">[en]</a><a href="#cite_note-multiref1-4">[4]</a>. К 300 г. да н.э. знак двух нахіленых кліноў ужываўся ў якасці запаўняльніка<a href="#cite_note-5">[5]</a><a href="#cite_note-6">[6]</a>. <div class="mw-heading mw-heading3"><h3 id="Дакалумбава_Амерыка">Дакалумбава Амерыка</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=10" title="Правіць раздзел: Дакалумбава Амерыка" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=10" title="Правіць зыходнік раздзела: Дакалумбава Амерыка">правіць зыходнік</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Cero_maya.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Cero_maya.svg/220px-Cero_maya.svg.png" decoding="async" width="220" height="109" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Cero_maya.svg/330px-Cero_maya.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Cero_maya.svg/440px-Cero_maya.svg.png 2x" data-file-width="303" data-file-height="150" /></a><figcaption>Нуль у мая</figcaption></figure> <a href="/w/index.php?title=%D0%9C%D0%B5%D0%B7%D0%B0%D0%B0%D0%BC%D0%B5%D1%80%D1%8B%D0%BA%D0%B0%D0%BD%D1%81%D0%BA%D1%96_%D0%BA%D0%B0%D0%BB%D0%B5%D0%BD%D0%B4%D0%B0%D1%80_%D0%B4%D0%BE%D1%9E%D0%B3%D0%B0%D0%B3%D0%B0_%D0%BF%D0%B0%D0%B4%D0%BB%D1%96%D0%BA%D1%83&action=edit&redlink=1" class="new" title="Мезаамерыканскі календар доўгага падліку (няма такой старонкі)">Мезаамерыканскі каляндар доўгага падліку</a><a href="https://en.wikipedia.org/wiki/Mesoamerican_Long_Count_calendar" class="extiw" title="en:Mesoamerican Long Count calendar">[en]</a>, распрацаваны ў паўднёва-цэнтральнай частцы Мексікі і Цэнтральнай Амерыцы, патрабаваў выкарыстання нуля ў якасці запаўняльніка ў сваёй <a href="/w/index.php?title=%D0%94%D0%B2%D0%B0%D1%86%D1%86%D0%B0%D1%82%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F&action=edit&redlink=1" class="new" title="Дваццатковая сістэма злічэння (няма такой старонкі)">дваццатковай</a><a href="https://en.wikipedia.org/wiki/Vigesimal" class="extiw" title="en:Vigesimal">[en]</a> пазіцыйнай сістэме злічэння. Многія гліфы, у тым ліку частковы <a href="/w/index.php?title=%D0%A7%D0%B0%D1%82%D1%8B%D1%80%D0%BE%D1%85%D0%BB%D1%96%D1%81%D0%BD%D1%96%D0%BA&action=edit&redlink=1" class="new" title="Чатырохліснік (няма такой старонкі)">чатырохліснік</a><a href="https://en.wikipedia.org/wiki/Quatrefoil" class="extiw" title="en:Quatrefoil">[en]</a>, выкарыстоўваліся ў якасці нулявога сімвала для запісу дат, найраннейшы з якіх (на Стэле 2 у Ч’япа-дэ-Корса, <a href="/wiki/%D0%A7%E2%80%99%D1%8F%D0%BF%D0%B0%D1%81" title="Ч’япас">Ч’япас</a>) датуецца 36 г. да н.э.<a href="#cite_note-7">[заўв 1]</a> Восем найраннейшых дат доўгага падліку з’яўляюцца па-за межамі рассялення мая<a href="#cite_note-8">[7]</a>, таму звычайна ўважаецца, што выкарыстанне нуля ў Амерыцы пачалося раней за мая і, магчыма, было вынаходніцтвам альмекаў<a href="#cite_note-9">[8]</a>. Многія з ранніх дат доўгага падліку былі знойдзены ў асяродку рассялення <a href="/wiki/%D0%90%D0%BB%D1%8C%D0%BC%D0%B5%D0%BA%D1%96" title="Альмекі">альмекаў</a>, хаця іх цывілізацыя знікла ў 4 стагоддзі да н.э., за некалькі стагоддзяў да найраннейшых вядомых дат доўгага падліку. Нягледзячы на тое, што нуль стаў неад’емнай часткай <a href="/w/index.php?title=%D0%9B%D1%96%D1%87%D0%B1%D1%8B_%D0%BC%D0%B0%D1%8F&action=edit&redlink=1" class="new" title="Лічбы мая (няма такой старонкі)">злічэння мая</a><a href="https://en.wikipedia.org/wiki/Maya_numerals" class="extiw" title="en:Maya numerals">[en]</a> з пустой чарапахападобнай «формай панцыра», якая часта выкарыстоўвалася для адлюстравання лічбы «нуль», мяркуецца, што гэта не паўплывала на сістэмы злічэння <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%80%D1%8B_%D0%A1%D0%B2%D0%B5%D1%82" title="Стары Свет">Старога Свету</a>. <a href="/wiki/%D0%9A%D1%96%D0%BF%D1%83" title="Кіпу">Кіпу</a>, прылада з шнуроў з вузламі, якая выкарыстоўвалася ў <a href="/wiki/%D0%86%D0%BC%D0%BF%D0%B5%D1%80%D1%8B%D1%8F_%D0%86%D0%BD%D0%BA%D0%B0%D1%9E" title="Імперыя Інкаў">Імперыі Інкаў</a> і папярэдніх грамадствах у рэгіёне <a href="/wiki/%D0%90%D0%BD%D0%B4%D1%8B" title="Анды">Анд</a> для запісу бухгалтарскіх і іншых лічбавых даных, адпавядае <a href="/wiki/%D0%94%D0%B7%D0%B5%D1%81%D1%8F%D1%82%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Дзесятковая сістэма злічэння">дзесятковай</a> пазіцыйнай сістэме. Нуль прадстаўлены адсутнасцю вузла ў адпаведным становішчы. <div class="mw-heading mw-heading3"><h3 id="Класічная_антычнасць">Класічная антычнасць</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=11" title="Правіць раздзел: Класічная антычнасць" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=11" title="Правіць зыходнік раздзела: Класічная антычнасць">правіць зыходнік</a>]</div> <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%80%D0%B0%D0%B6%D1%8B%D1%82%D0%BD%D1%8B%D1%8F_%D0%B3%D1%80%D1%8D%D0%BA%D1%96" class="mw-redirect" title="Старажытныя грэкі">Старажытныя грэкі</a> не мелі сімвала для нуля (<a href="/wiki/%D0%A1%D1%82%D0%B0%D1%80%D0%B0%D0%B6%D1%8B%D1%82%D0%BD%D0%B0%D0%B3%D1%80%D1%8D%D1%87%D0%B0%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B2%D0%B0" title="Старажытнагрэчаская мова">стар.-грэч.</a>: μηδέν, вымаўляецца як «мідэн») і не выкарыстоўвалі лічбавы запаўняльнік для яго<a href="#cite_note-10">[9]</a>. Паводле матэматыка <a href="/w/index.php?title=%D0%A7%D0%B0%D1%80%D0%BB%D0%B7_%D0%A1%D0%B0%D0%B9%D1%84%D1%8D&action=edit&redlink=1" class="new" title="Чарлз Сайфэ (няма такой старонкі)">Чарлза Сайфэ</a><a href="https://en.wikipedia.org/wiki/Charles_Seife" class="extiw" title="en:Charles Seife">[en]</a>, старажытныя грэкі сапраўды пачалі карыстацца вавілонскім нулём для прац па астраноміі пасля 500 г. да н.э., прадстаўляючы яго малой грэчаскай літарай ό (<a href="/wiki/%D0%9E_%D0%BC%D1%96%D0%BA%D1%80%D0%BE%D0%BD" title="О мікрон">о мікрон</a>)<a href="#cite_note-Seife2000-11">[10]</a>. Тым не менш, пасля выкарыстання вавілонскага нуля для астранамічных разлікаў яны звычайна пераводзілі лічбы назад у <a href="/wiki/%D0%93%D1%80%D1%8D%D1%87%D0%B0%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Грэчаская сістэма злічэння">грэчаскія</a><a href="#cite_note-Seife2000-11">[10]</a>. Грэкі, здавалася, мелі філасофскую апазіцыю да выкарыстання нуля ў якасці ліку<a href="#cite_note-Seife2000-11">[10]</a>. Іншыя навукоўцы прысвойваюць грэчаскаму частковаму прыняццю вавілонскага нуля пазнейшую дату, так навуковец Андрэас Нідэр датуе гэта пасля 400 г. да н.э., а матэматык Роберт Каплан называе перыяд пасля <a href="/w/index.php?title=%D0%92%D0%BE%D0%B9%D0%BD%D1%8B_%D0%90%D0%BB%D1%8F%D0%BA%D1%81%D0%B0%D0%BD%D0%B4%D1%80%D0%B0_%D0%9C%D0%B0%D0%BA%D0%B5%D0%B4%D0%BE%D0%BD%D1%81%D0%BA%D0%B0%D0%B3%D0%B0&action=edit&redlink=1" class="new" title="Войны Аляксандра Македонскага (няма такой старонкі)">заваёў Аляксандра Македонскага</a><a href="https://en.wikipedia.org/wiki/Wars_of_Alexander_the_Great" class="extiw" title="en:Wars of Alexander the Great">[en]</a><a href="#cite_note-Nieder2019-12">[11]</a><a href="#cite_note-Kaplan1999-13">[12]</a> . Грэкі, здаецца, не былі ўпэўненыя ў статусе нуля як ліку. Некаторыя з іх задаваліся пытаннем: «Як небыццё можа быць?», што прывяло да філасофскіх, а ў перыяд <a href="/wiki/%D0%A1%D1%8F%D1%80%D1%8D%D0%B4%D0%BD%D1%8F%D0%B2%D0%B5%D1%87%D1%87%D0%B0" class="mw-redirect" title="Сярэднявечча">сярэднявечча</a> і рэлігійных аргументаў аб прыродзе і існаванні нуля і <a href="/wiki/%D0%92%D0%B0%D0%BA%D1%83%D1%83%D0%BC" title="Вакуум">вакууму</a>. <a href="/w/index.php?title=%D0%90%D0%BF%D0%BE%D1%80%D1%8B%D1%96_%D0%97%D1%8F%D0%BD%D0%BE%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Апорыі Зянона (няма такой старонкі)">Апорыі</a><a href="https://en.wikipedia.org/wiki/Zeno%27s_paradoxes" class="extiw" title="en:Zeno's paradoxes">[en]</a> <a href="/wiki/%D0%97%D1%8F%D0%BD%D0%BE%D0%BD_%D0%AD%D0%BB%D0%B5%D0%B9%D1%81%D0%BA%D1%96" title="Зянон Элейскі">Зянона Элейскага</a> шмат у чым грунтуюцца на няпэўнай інтэрпрэтацыі нуля<a href="#cite_note-14">[13]</a>. <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:P._Lund,_Inv._35a.jpg" class="mw-file-description"><img alt="Фрагмент папірусу з выразным грэчаскім пісьмом, у правым ніжнім куце намаляваны малюсенькі нуль з двухканцовай стрэлкай над ім" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/P._Lund%2C_Inv._35a.jpg/300px-P._Lund%2C_Inv._35a.jpg" decoding="async" width="300" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/P._Lund%2C_Inv._35a.jpg/450px-P._Lund%2C_Inv._35a.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/1/1b/P._Lund%2C_Inv._35a.jpg 2x" data-file-width="550" data-file-height="300" /></a><figcaption>Прыклад ранняга грэчаскага сімвала нуля (правы ніжні кут) з папіруса 2-га стагоддзя</figcaption></figure> К 150 г. нашай эры <a href="/wiki/%D0%9F%D1%82%D0%B0%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" class="mw-redirect" title="Пталемей">Пталемей</a> пад уплывам <a href="/wiki/%D0%93%D1%96%D0%BF%D0%B0%D1%80%D1%85" title="Гіпарх">Гіпарха</a> і <a href="/wiki/%D0%92%D0%B0%D0%B2%D1%96%D0%BB%D0%BE%D0%BD%D1%96%D1%8F" title="Вавілонія">вавілонян</a> выкарыстоўваў сімвал нуля <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {\circ }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>∘</mo> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {\circ }}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2874d4b13af6fd8c427d7a148214e1cb07920a06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.125ex; margin-bottom: -0.297ex; width:1.277ex; height:2.176ex;" alt="{\displaystyle {\overline {\circ }}}"><a href="#cite_note-15">[14]</a><a href="#cite_note-Mercier-16">[15]</a> у сваёй працы па <a href="/wiki/%D0%A2%D1%8D%D0%B0%D1%80%D1%8D%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D0%B0%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%BE%D0%BC%D1%96%D1%8F" title="Тэарэтычная астраномія">тэарэтычнай астраноміі</a> пад назвай Syntaxis Mathematica, таксама вядомай як <a href="/w/index.php?title=%D0%90%D0%BB%D1%8C%D0%BC%D0%B0%D0%B3%D0%B5%D1%81%D1%82&action=edit&redlink=1" class="new" title="Альмагест (няма такой старонкі)">Альмагест</a><a href="https://en.wikipedia.org/wiki/Almagest" class="extiw" title="en:Almagest">[en]</a><a href="#cite_note-Ptolemy-17">[16]</a>. Гэты эліністычны нуль быў, мабыць, самым раннім дакументальна пацверджаным выкарыстаннем лічбы, якая прадстаўляе нуль, у Старым Свеце<a href="#cite_note-18">[17]</a>. Пталамей шмат разоў выкарыстоўваў яго ў сваім Альмагесце (VI.8) для апісання <a href="/wiki/%D0%A1%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%B0%D0%B5_%D0%B7%D0%B0%D1%86%D1%8C%D0%BC%D0%B5%D0%BD%D0%BD%D0%B5" title="Сонечнае зацьменне">сонечных</a> і <a href="/wiki/%D0%9C%D0%B5%D1%81%D1%8F%D1%87%D0%BD%D0%B0%D0%B5_%D0%B7%D0%B0%D1%86%D1%8C%D0%BC%D0%B5%D0%BD%D0%BD%D0%B5" title="Месячнае зацьменне">месячных зацьменняў</a>. Самае ранняе выкарыстанне нуля пры <a href="/w/index.php?title=%D0%9F%D0%B0%D1%81%D1%85%D0%B0%D0%BB%D1%96%D1%8F&action=edit&redlink=1" class="new" title="Пасхалія (няма такой старонкі)">вылічэнні даты юліянскага Вялікадня</a><a href="https://en.wikipedia.org/wiki/Date_of_Easter" class="extiw" title="en:Date of Easter">[en]</a> адбылося да 311 года н.э., у першым запісе ў табліцы <a href="/w/index.php?title=%D0%AD%D0%BF%D0%B0%D0%BA%D1%82%D0%B0&action=edit&redlink=1" class="new" title="Эпакта (няма такой старонкі)">эпактаў</a><a href="https://en.wikipedia.org/wiki/Epact" class="extiw" title="en:Epact">[en]</a>, захаванай у <a href="/wiki/%D0%AD%D1%84%D1%96%D0%BE%D0%BF%D1%96%D1%8F" title="Эфіопія">эфіопскім</a> дакуменце за 311—369 гады, з выкарыстаннем <a href="/w/index.php?title=%D0%93%D0%B5%D1%8D%D0%B7&action=edit&redlink=1" class="new" title="Геэз (няма такой старонкі)">геэзскага</a><a href="https://en.wikipedia.org/wiki/Ge%CA%BDez" class="extiw" title="en:Geʽez">[en]</a> слова для «нішто» разам з геэзскімі лічбамі (на аснове грэчаскіх лічбаў). Табліца была перакладзена з эквівалентнай табліцы, апублікаванай <a href="/w/index.php?title=%D0%90%D0%BB%D0%B5%D0%BA%D1%81%D0%B0%D0%BD%D0%B4%D1%80%D1%8B%D0%B9%D1%81%D0%BA%D0%B0%D1%8F_%D1%86%D0%B0%D1%80%D0%BA%D0%B2%D0%B0&action=edit&redlink=1" class="new" title="Александрыйская царква (няма такой старонкі)">Александрыйскай царквой</a><a href="https://en.wikipedia.org/wiki/Church_of_Alexandria" class="extiw" title="en:Church of Alexandria">[en]</a> на <a href="/w/index.php?title=%D0%A1%D1%8F%D1%80%D1%8D%D0%B4%D0%BD%D1%8F%D0%B3%D1%80%D1%8D%D1%87%D0%B0%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B2%D0%B0&action=edit&redlink=1" class="new" title="Сярэднягрэчаская мова (няма такой старонкі)">сярэднягрэчаскай мове</a><a href="https://en.wikipedia.org/wiki/Medieval_Greek" class="extiw" title="en:Medieval Greek">[en]</a><a href="#cite_note-Neugebauer-19">[18]</a>. Тое ж фіксуецца ў 525 годзе ў эквівалентнай табліцы, пры перакладзе якой на лацінскую <a href="/wiki/%D0%94%D1%8B%D1%8F%D0%BD%D1%96%D1%81%D1%96%D0%B9_%D0%9C%D0%B0%D0%BB%D1%8B" title="Дыянісій Малы">Дыянісій Малы</a> ўжываў слова nulla ў адным шэрагу з <a href="/wiki/%D0%A0%D1%8B%D0%BC%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Рымская сістэма злічэння">рымскімі лічбамі</a><a href="#cite_note-Dionysius-20">[19]</a>. Калі дзяленне давала нуль у якасці рэшты, выкарыстоўваўся nihil, што азначае «нічога». Гэтыя сярэднявечныя нулі выкарыстоўвалі ўсе наступныя сярэднявечныя вылічальнікі Вялікадня. Ініцыял «N» выкарыстоўваў у якасці нулявога сімвала ў табліцы рымскіх лічбаў <a href="/wiki/%D0%91%D0%B5%D0%B4%D0%B0_%D0%92%D1%8F%D0%BB%D0%B5%D0%B1%D0%BD%D1%8B" title="Беда Вялебны">Беда Вялебны</a> або яго калегі каля 725 г. н.э.<a href="#cite_note-zero-21">[20]</a> <div class="mw-heading mw-heading3"><h3 id="Кітай">Кітай</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=12" title="Правіць раздзел: Кітай" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=12" title="Правіць зыходнік раздзела: Кітай">правіць зыходнік</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Zero_in_Rod_Calculus.png" class="mw-file-description"><img alt="Пяць клетак злева направа ўтрымліваюць Т-падобную форму, пустую клетку, тры вертыкальныя палоскі, тры ніжнія гарызантальныя палоскі з перавернутай шырокай Т-формай уверсе і яшчэ адну пустую клетку. Лічбы злева направа ніжэй — шэсць, нуль, тры, дзевяць і нуль" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Zero_in_Rod_Calculus.png/220px-Zero_in_Rod_Calculus.png" decoding="async" width="220" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Zero_in_Rod_Calculus.png/330px-Zero_in_Rod_Calculus.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Zero_in_Rod_Calculus.png/440px-Zero_in_Rod_Calculus.png 2x" data-file-width="804" data-file-height="293" /></a><figcaption>Адлюстраванне нуля з дапамогай кітайскіх <a href="/w/index.php?title=%D0%9B%D1%96%D1%87%D1%8B%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F_%D0%BF%D0%B0%D0%BB%D0%B0%D1%87%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Лічыльныя палачкі (няма такой старонкі)">лічыльных палачак</a><a href="https://en.wikipedia.org/wiki/Counting_rods" class="extiw" title="en:Counting rods">[en]</a> на прыкладзе з «Гісторыі матэматыкі». Пустая клетка выкарыстоўваецца для прадстаўлення нуля<a href="#cite_note-Hodgkin-22">[21]</a>.</figcaption></figure> <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%D1%8B_%D0%B4%D0%B0%D0%BF%D0%B0%D0%BC%D0%BE%D0%B6%D0%BD%D1%96%D0%BA_%D0%A1%D1%83%D0%BD%D1%8C%D1%86%D0%B7%D1%8B&action=edit&redlink=1" class="new" title="Матэматычны дапаможнік Суньцзы (няма такой старонкі)">Матэматычны дапаможнік Суньцзы</a><a href="https://en.wikipedia.org/wiki/Sunzi_Suanjing" class="extiw" title="en:Sunzi Suanjing">[en]</a>, датаваны, паводле ацэнак, з 1-е па 5-е стагоддзямі нашай эры, і японскія запісы, датаваныя 18-м стагоддзем, апісваюць, як кітайская сістэма <a href="/w/index.php?title=%D0%9B%D1%96%D1%87%D1%8B%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F_%D0%BF%D0%B0%D0%BB%D0%B0%D1%87%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Лічыльныя палачкі (няма такой старонкі)">лічыльных палачак</a><a href="https://en.wikipedia.org/wiki/Counting_rods" class="extiw" title="en:Counting rods">[en]</a> у 4-м стагоддзі да н.э. дазваляла выконваць дзесятковыя вылічэнні. Як адзначаецца ў <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%D1%8B_%D0%B4%D0%B0%D0%BF%D0%B0%D0%BC%D0%BE%D0%B6%D0%BD%D1%96%D0%BA_%D0%A1%D1%8F%D1%85%D0%BE%D1%83_%D0%AF%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Матэматычны дапаможнік Сяхоу Яна (няма такой старонкі)">матэматычным дапаможніку Сяхоу Яна</a><a href="https://en.wikipedia.org/wiki/Xiahou_Yang_Suanjing" class="extiw" title="en:Xiahou Yang Suanjing">[en]</a> (425—468 гг. н. э.), каб памножыць або падзяліць лік на 10, 100, 1000 ці 10000, усё, што трэба зрабіць, трымаючы палачкі на дошцы для падліку, гэта перасунуць іх наперад, або назад, на адну, дзве, тры або чатыры клеткі<a href="#cite_note-23">[22]</a>, Згодна з «Гісторыяй матэматыкі», палачкі «давалі дзесятковае прадстаўленне ліку, дзе пустая клетка абазначала нуль»<a href="#cite_note-Hodgkin-22">[21]</a>. Сістэма лічыльных палачак лічыцца <a href="/w/index.php?title=%D0%9F%D0%B0%D0%B7%D1%96%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D1%8F_%D0%BD%D0%B0%D1%82%D0%B0%D1%86%D1%8B%D1%8F&action=edit&redlink=1" class="new" title="Пазіцыйная натацыя (няма такой старонкі)">пазіцыйнай сістэмай запісу</a><a href="https://en.wikipedia.org/wiki/Positional_notation" class="extiw" title="en:Positional notation">[en]</a><a href="#cite_note-24">[23]</a>. У 690 г. н. э. імператрыца <a href="/wiki/%D0%A3_%D0%A6%D0%B7%D1%8D%D1%86%D1%8F%D0%BD%D1%8C" title="У Цзэцянь">У Цзэцянь</a> абнародавала <a href="/w/index.php?title=%D0%86%D0%B5%D1%80%D0%BE%D0%B3%D0%BB%D1%96%D1%84%D1%8B_%D1%96%D0%BC%D0%BF%D0%B5%D1%80%D0%B0%D1%82%D1%80%D1%8B%D1%86%D1%8B_%D0%A3&action=edit&redlink=1" class="new" title="Іерогліфы імператрыцы У (няма такой старонкі)">іерогліфы</a><a href="https://en.wikipedia.org/wiki/Chinese_characters_of_Empress_Wu" class="extiw" title="en:Chinese characters of Empress Wu">[en]</a>, адным з якіх быў «〇» (сін); першапачаткова іерогліф абазначаў зорку, а пазней стаў выкарыстоўвацца для запісу нуля. Нуль у той час разглядаўся не як лік, а як «пустая пазіцыя»<a href="#cite_note-Crossley-25">[24]</a>. <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%D1%8B_%D1%82%D1%80%D0%B0%D0%BA%D1%82%D0%B0%D1%82_%D1%83_%D0%B4%D0%B7%D0%B5%D0%B2%D1%8F%D1%86%D1%96_%D1%80%D0%B0%D0%B7%D0%B4%D0%B7%D0%B5%D0%BB%D0%B0%D1%85&action=edit&redlink=1" class="new" title="Матэматычны трактат у дзевяці раздзелах (няма такой старонкі)">Матэматычны трактат у дзевяці раздзелах</a><a href="https://en.wikipedia.org/wiki/Mathematical_Treatise_in_Nine_Sections" class="extiw" title="en:Mathematical Treatise in Nine Sections">[en]</a> <a href="/wiki/%D0%A6%D1%8B%D0%BD%D1%8C_%D0%A6%D0%B7%D1%8E%D1%88%D0%B0%D0%B0" title="Цынь Цзюшаа">Цынь Цзюшаа</a> 1247 года з’яўляецца найстарэйшым захаваным кітайскім матэматычным тэкстам, які выкарыстоўвае круглы сімвал для нуля<a href="#cite_note-Qin-26">[25]</a>. Кітайскія аўтары былі знаёмыя з ідэяй адмоўных лікаў у часы <a href="/wiki/%D0%86%D0%BC%D0%BF%D0%B5%D1%80%D1%8B%D1%8F_%D0%A5%D0%B0%D0%BD%D1%8C" title="Імперыя Хань">дынастыі Хань</a> (2 стагоддзе нашай эры), як відаць у <a href="/w/index.php?title=%D0%94%D0%B7%D0%B5%D0%B2%D1%8F%D1%86%D1%8C_%D1%80%D0%B0%D0%B7%D0%B4%D0%B7%D0%B5%D0%BB%D0%B0%D1%9E_%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D0%B3%D0%B0_%D0%BC%D0%B0%D1%81%D1%82%D0%B0%D1%86%D1%82%D0%B2%D0%B0&action=edit&redlink=1" class="new" title="Дзевяць раздзелаў матэматычнага мастацтва (няма такой старонкі)">Дзевяці раздзелах матэматычнага мастацтва</a><a href="https://en.wikipedia.org/wiki/The_Nine_Chapters_on_the_Mathematical_Art" class="extiw" title="en:The Nine Chapters on the Mathematical Art">[en]</a><a href="#cite_note-struik33-27">[26]</a>. <div class="mw-heading mw-heading3"><h3 id="Індыя">Індыя</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=13" title="Правіць раздзел: Індыя" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=13" title="Правіць зыходнік раздзела: Індыя">правіць зыходнік</a>]</div> <a href="/w/index.php?title=%D0%9F%D1%96%D0%BD%D0%B3%D0%B0%D0%BB%D0%B0&action=edit&redlink=1" class="new" title="Пінгала (няма такой старонкі)">Пінгала</a><a href="https://en.wikipedia.org/wiki/Pingala" class="extiw" title="en:Pingala">[en]</a> (прыблізна 3-е/2-е стагоддзі да н.э.<a href="#cite_note-plofker-28">[27]</a>), даследуючы <a href="/wiki/%D0%9C%D0%B5%D1%82%D1%80_(%D0%B2%D0%B5%D1%80%D1%88%D0%B0%D1%81%D0%BA%D0%BB%D0%B0%D0%B4%D0%B0%D0%BD%D0%BD%D0%B5)" title="Метр (вершаскладанне)">метр</a> санскрыцкіх вершаў<a href="#cite_note-29">[28]</a>, выкарыстоўваў <a href="/wiki/%D0%94%D0%B2%D0%B0%D0%B9%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Двайковая сістэма злічэння">двайковыя лікі</a> ў выглядзе кароткіх і доўгіх складоў (апошнія роўныя па даўжыні двум кароткім складам) — запіс, падобны да <a href="/wiki/%D0%90%D0%B7%D0%B1%D1%83%D0%BA%D0%B0_%D0%9C%D0%BE%D1%80%D0%B7%D1%8D" title="Азбука Морзэ">азбукі Морзэ</a><a href="#cite_note-30">[29]</a>. Пінгала яўна выкарыстоўваў <a href="/wiki/%D0%A1%D0%B0%D0%BD%D1%81%D0%BA%D1%80%D1%8B%D1%82" title="Санскрыт">санскрыцкае</a> слова <a href="/w/index.php?title=%D0%A8%D1%83%D0%BD%D1%8C%D1%8F%D1%82%D0%B0&action=edit&redlink=1" class="new" title="Шуньята (няма такой старонкі)">шунья</a><a href="https://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81" class="extiw" title="en:Śūnyatā">[en]</a> для абазначэння нуля<a href="#cite_note-plofker-28">[27]</a>. Канцэпцыя нуля як пісьмовай лічбы ў дзесятковай пазіцыйнай натацыі была распрацавана ў Індыі<a href="#cite_note-bourbaki46-31">[30]</a>. Сімвал нуля, вялікая кропка, якая, верагодна, з’яўляецца папярэднікам распаўсюджанага цяпер пустога сімвала, выкарыстоўваецца ў <a href="/w/index.php?title=%D0%A0%D1%83%D0%BA%D0%B0%D0%BF%D1%96%D1%81_%D0%91%D0%B0%D1%85%D1%88%D0%B0%D0%BB%D1%96&action=edit&redlink=1" class="new" title="Рукапіс Бахшалі (няма такой старонкі)">рукапісе Бахшалі</a><a href="https://en.wikipedia.org/wiki/Bakhshali_manuscript" class="extiw" title="en:Bakhshali manuscript">[en]</a>, практычным дапаможніку па арыфметыцы для гандляроў<a href="#cite_note-Weiss-32">[31]</a>. У 2017 годзе <a href="/wiki/%D0%A0%D0%B0%D0%B4%D1%8B%D0%B5%D0%B2%D1%83%D0%B3%D0%BB%D1%8F%D1%80%D0%BE%D0%B4%D0%BD%D0%B0%D0%B5_%D0%B4%D0%B0%D1%82%D0%B0%D0%B2%D0%B0%D0%BD%D0%BD%D0%B5" title="Радыевугляроднае датаванне">радыевугляроднае датаванне</a> паказала, што тры ўзоры з рукапісу паходзяць з трох розных стагоддзяў: з 224—383, 680—779 і 885—993 гг. н.э. Невядома, якім чынам фрагменты <a href="/wiki/%D0%91%D1%8F%D1%80%D0%BE%D1%81%D1%82%D0%B0" title="Бяроста">берасцянай</a> кары розных стагоддзяў, якія складалі рукапіс, былі ўкладзеныя разам<a href="#cite_note-33">[32]</a><a href="#cite_note-34">[33]</a><a href="#cite_note-35">[34]</a>. <a href="/w/index.php?title=%D0%9B%D0%BE%D0%BA%D0%B0%D0%B2%D1%96%D0%B1%D1%85%D0%B0%D0%B3%D0%B0&action=edit&redlink=1" class="new" title="Локавібхага (няма такой старонкі)">Локавібхага</a><a href="https://en.wikipedia.org/wiki/Lokavibhaga" class="extiw" title="en:Lokavibhaga">[en]</a>, <a href="/wiki/%D0%94%D0%B6%D0%B0%D0%B9%D0%BD%D1%96%D0%B7%D0%BC" title="Джайнізм">джайнісцкі</a> тэкст па <a href="/wiki/%D0%9A%D0%B0%D1%81%D0%BC%D0%B0%D0%BB%D0%BE%D0%B3%D1%96%D1%8F" title="Касмалогія">касмалогіі</a> 458 г. н.э. (эра Сака 380), што захаваўся ў сярэднявечным санскрыцкім перакладзе з <a href="/wiki/%D0%9F%D1%80%D0%B0%D0%BA%D1%80%D1%8B%D1%82" title="Пракрыт">пракрыту</a>, выкарыстоўвае дзесятковую <a href="/w/index.php?title=%D0%9F%D0%B0%D0%B7%D1%96%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D1%8F_%D0%BD%D0%B0%D1%82%D0%B0%D1%86%D1%8B%D1%8F&action=edit&redlink=1" class="new" title="Пазіцыйная натацыя (няма такой старонкі)">пазіцыйную</a><a href="https://en.wikipedia.org/wiki/Positional_notation" class="extiw" title="en:Positional notation">[en]</a> сістэму з нулём. У гэтым тэксце шунья («пусты») таксама выкарыстоўваецца для абазначэння нуля<a href="#cite_note-36">[35]</a>. <a href="/w/index.php?title=%D0%90%D1%80%E2%80%99%D1%8F%D0%B1%D1%85%D0%B0%D1%82%D1%8B%D1%8F&action=edit&redlink=1" class="new" title="Ар’ябхатыя (няма такой старонкі)">Ар’ябхатыя</a><a href="https://en.wikipedia.org/wiki/Aryabhatiya" class="extiw" title="en:Aryabhatiya">[en]</a> (каля 500 г.) сцвярджае, што «ад месца да месца кожнае ў дзесяць разоў перавышае папярэдняе»<a href="#cite_note-Aryab-37">[36]</a><a href="#cite_note-38">[37]</a><a href="#cite_note-39">[38]</a>. Правілы, якія рэгулююць выкарыстанне нуля, з’явіліся ў <a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D1%81%D0%BF%D1%83%D1%82%D0%B0%D1%81%D1%96%D0%B4%D1%85%D0%B0%D0%BD%D1%82%D0%B0&action=edit&redlink=1" class="new" title="Брахмаспутасідханта (няма такой старонкі)">Брахмаспутасідханце</a><a href="https://en.wikipedia.org/wiki/Br%C4%81hmasphu%E1%B9%ADasiddh%C4%81nta" class="extiw" title="en:Brāhmasphuṭasiddhānta">[en]</a> <a href="/wiki/%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта">Брахмагупты</a> (7-е стагоддзе), дзе гаворыцца, што сума нуля з самім сабой роўная нулю, і згадваецца дзяленне нуля і <a href="/w/index.php?title=%D0%94%D0%B7%D1%8F%D0%BB%D0%B5%D0%BD%D0%BD%D0%B5_%D0%BD%D0%B0_%D0%BD%D1%83%D0%BB%D1%8C&action=edit&redlink=1" class="new" title="Дзяленне на нуль (няма такой старонкі)">на нуль</a><a href="https://en.wikipedia.org/wiki/Division_by_zero" class="extiw" title="en:Division by zero">[en]</a><a href="#cite_note-brahmagupta-40">[39]</a><a href="#cite_note-Kaplan-41">[40]</a>: <table style="margin:auto; border-collapse:collapse; background-color:transparent; color:inherit; border-style:none;"> <tbody><tr> <td style="width:30px; vertical-align:top; padding-right:10px;"><img alt=""" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Aquote1.png/30px-Aquote1.png" decoding="async" width="30" height="23" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/44/Aquote1.png 1.5x" data-file-width="40" data-file-height="30" /> </td> <td><cite>Дадатны або адмоўны лік пры дзяленні на нуль утварае дроб з нулём у якасці назоўніка. Нуль, падзелены на адмоўны або дадатны лік, альбо роўны нулю, альбо выражаецца ў выглядзе дробу з нулём у якасці лічніка і канечнай велічыні ў якасці назоўніка. Нуль, падзелены на нуль, — гэта нуль.</cite><div style="clear:both;"></div><div style="float:right"><a href="/wiki/%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта">Брахмагупта</a></div> </td> <td style="width:30px; vertical-align:bottom; padding-left:10px;"><img alt=""" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Aquote2.png/30px-Aquote2.png" decoding="async" width="30" height="23" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/49/Aquote2.png 1.5x" data-file-width="40" data-file-height="30" /> </td></tr></tbody></table> Першае вядомае выкарыстанне <a href="/wiki/%D0%93%D0%BB%D1%96%D1%84" title="Гліф">гліфа</a> нуль у сучасным выглядзе маленькага круга, знойдзена на каменным надпісе ў храме <a href="/w/index.php?title=%D0%A5%D1%80%D0%B0%D0%BC_%D0%A7%D0%B0%D1%82%D1%83%D1%80%D0%B1%D1%85%D1%83%D0%B4%D0%B6,_%D0%93%D0%B2%D0%B0%D0%BB%D1%96%D1%91%D1%80&action=edit&redlink=1" class="new" title="Храм Чатурбхудж, Гваліёр (няма такой старонкі)">Чатурбхудж</a><a href="https://en.wikipedia.org/wiki/Chaturbhuj_Temple,_Gwalior" class="extiw" title="en:Chaturbhuj Temple, Gwalior">[en]</a>, <a href="/wiki/%D0%93%D0%B2%D0%B0%D0%BB%D1%96%D1%91%D1%80" title="Гваліёр">Гваліёр</a>, у Індыі, датаваным 876 г.<a href="#cite_note-42">[41]</a><a href="#cite_note-43">[42]</a> <div class="mw-heading mw-heading3"><h3 id="Сярэднявечча">Сярэднявечча</h3>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=14" title="Правіць раздзел: Сярэднявечча" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=14" title="Правіць зыходнік раздзела: Сярэднявечча">правіць зыходнік</a>]</div> <div class="mw-heading mw-heading4"><h4 id="З'яўленне_ў_ісламскім_свеце">З'яўленне ў ісламскім свеце</h4>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=15" title="Правіць раздзел: З'яўленне ў ісламскім свеце" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=15" title="Правіць зыходнік раздзела: З'яўленне ў ісламскім свеце">правіць зыходнік</a>]</div> <a href="/wiki/%D0%90%D1%80%D0%B0%D0%B1%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B2%D0%B0" title="Арабская мова">Арабскамоўная</a> навука збольшага грунтавалася на <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">грэчаскай</a><a href="#cite_note-44">[43]</a> з індускімі ўплывамі<a href="#cite_note-Durant-45">[44]</a>. У 773 годзе на загад <a href="/w/index.php?title=%D0%90%D0%BB%D1%8C-%D0%9C%D0%B0%D0%BD%D1%81%D1%83%D1%80&action=edit&redlink=1" class="new" title="Аль-Мансур (няма такой старонкі)">Аль-Мансура</a><a href="https://en.wikipedia.org/wiki/al-Mansur" class="extiw" title="en:al-Mansur">[en]</a> былі зробленыя пераклады многіх старажытных трактатаў, у тым ліку грэчаскіх, рымскіх, індыйскіх і іншых. У 813 г. н.э. <a href="/wiki/%D0%9F%D0%B5%D1%80%D1%81%D1%96%D1%8F" title="Персія">персідскі</a> матэматык <a href="/wiki/%D0%9C%D1%83%D1%85%D0%B0%D0%BC%D0%B0%D0%B4_%D0%90%D0%BB%D1%8C-%D0%A5%D0%B0%D1%80%D1%8D%D0%B7%D0%BC%D1%96" title="Мухамад Аль-Харэзмі">Мухамад Аль-Харэзмі</a> падрыхтаваў астранамічныя табліцы, у якіх карыстаўся індыйскімі лікамі<a href="#cite_note-Durant-45">[44]</a>. Каля 825 г. ён апублікаваў кнігу ў якой сумяшчалася грэцкая і індуская навука, а таксама яго ўласны ўнёсак у матэматыку, у тым ліку тлумачэнне выкарыстання нуля<a href="#cite_note-46">[45]</a>. Гэтая кніга была 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">лаціну</a> ў XII ст. пад назвай Algoritmi de numero Indorum (Аль-Харэзмі пра лікі індыйцаў). Слова "Algoritmi" было перакладчыцкай лацінізацыяй імя Аль-Харэзмі, і з тых пор пачало набываць значэнне якой-кольвек арыфметычнай працэдуры<a href="#cite_note-Durant-45">[44]</a>. У 976 годзе Мухамад аль-Харэзмі сцвярджаў, што калі ў падліках на месцы дзясяткаў не з'яўляецца лік, трэба выкарыстоўваць маленькі кружок, «каб захаваць радкі». Гэты кружок называўся ṣifr<a href="#cite_note-47">[46]</a>. <div class="mw-heading mw-heading4"><h4 id="З'яўленне_ў_Еўропе">З'яўленне ў Еўропе</h4>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=16" title="Правіць раздзел: З'яўленне ў Еўропе" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=16" title="Правіць зыходнік раздзела: З'яўленне ў Еўропе">правіць зыходнік</a>]</div> Дзесятковая <a href="/w/index.php?title=%D0%86%D0%BD%D0%B4%D0%B0-%D0%B0%D1%80%D0%B0%D0%B1%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F&action=edit&redlink=1" class="new" title="Інда-арабская сістэма злічэння (няма такой старонкі)">інда-арабская сістэма злічэння</a><a href="https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system" class="extiw" title="en:Hindu–Arabic numeral system">[en]</a> патрапіла ў Заходнюю Еўропу ў XI ст. праз <a href="/wiki/%D0%90%D0%BB%D1%8C-%D0%90%D0%BD%D0%B4%D0%B0%D0%BB%D1%83%D1%81" title="Аль-Андалус">Аль-Андалус</a> ад іспанскіх <a href="/wiki/%D0%9C%D1%83%D1%81%D1%83%D0%BB%D1%8C%D0%BC%D0%B0%D0%BD%D0%B5" title="Мусульмане">мусульман</a>, <a href="/wiki/%D0%9C%D0%B0%D1%9E%D1%80%D1%8B" title="Маўры">маўраў</a>, разам з класічнай <a href="/wiki/%D0%90%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%BE%D0%BC%D1%96%D1%8F" title="Астраномія">астраноміяй</a> і такімі інструментамі як <a href="/wiki/%D0%90%D1%81%D1%82%D1%80%D0%B0%D0%BB%D1%8F%D0%B1%D1%96%D1%8F" title="Астралябія">астралябія</a>. Вяртанне забытай навукі ў каталіцкую Еўропу прыпісваецца <a href="/wiki/%D0%A1%D1%96%D0%BB%D1%8C%D0%B2%D0%B5%D1%81%D1%82%D1%80_II" title="Сільвестр II">Герберту Арыльякскаму</a>. З гэтай прычыны лічбы сталі вядомыя ў Еўропе як "арабскія лічбы". Італьянскі матэматык <a href="/wiki/%D0%A4%D1%96%D0%B1%D0%B0%D0%BD%D0%B0%D1%87%D1%8B" title="Фібаначы">Фібаначы</a>, або Леанарда Пізанскі, адыграў важную ролю ў распаўсюдзе сістэмы лікаў у Еўрапейскай матэматыцы, напісаўшы ў 1202 г.: <blockquote>Пасля прызначэння майго бацькі на радзіме дзяржаўным чыноўнікам на мытні Буджа для пізанскіх гандляроў, якія тоўпіліся ля яе, ён узяў на сябе кіраўніцтва; і для карысці і зручнасці, перавёз мяне малога да сябе і хацеў, каб я прысвяціў сябе і быў навучаны лічэнню некаторы час. Там, пасля майго знаёмства, як следства цудоўнага навучання майстэрству, з дзевяццю лічбамі індусаў, гэтае майстэрства вельмі спадабалася мне перад усімі іншымі, і я зразумеў, што ўсе яго аспекты вывучаліся ў Егіпце, Сірыі, Грэцыі, Сіцыліі і Правансе з іх рознымі метадамі. Я працягваў паглыбленае вывучэнне і навучыўся кампрамісам у спрэчках. Але нават усё гэта, і алгарызм, як і майстэрства Піфагора, я лічыў ледзь не памылкай у параўнанні з метадам <a href="/wiki/%D0%86%D0%BD%D0%B4%D1%83%D1%96%D0%B7%D0%BC" title="Індуізм">індусаў</a> (Modus Indorum). Дзеля таго я больш строга прытрымліваўся гэтага індускага метаду і больш рупліва стараўся яго вывучаць, адначасова дадаючы некаторыя рэчы з майго ўласнага разумення і ўстаўляючы таксама некаторыя рэчы з тонкасцей геаметрычнага майстэрства Эўкліда. Я імкнуўся скласці гэтую кнігу як мага больш зразумелай, падзяліўшы яе на пятнаццаць раздзелаў. Амаль усё, што я прадставіў, я паказаў з дакладнымі доказамі, каб тыя, хто далей паглыбляецца ў гэтую навуку з яе найвыдатнейшым метадам, маглі атрымаць інструкцыі, а таксама каб лацінскі народ не быў пазбаўлены яе, як да гэтага часу. Калі я выпадкова прапусціў што-небудзь больш-менш належнае або неабходнае, прашу паблажлівасці, бо няма нікога, хто быў бы беззаганным і цалкам прадбачлівым ва ўсім. Дзевяць індыйскіх лічбаў: 9 8 7 6 5 4 3 2 1. З дапамогай гэтых дзевяці лічбаў і са знакам 0 ... можа быць запісаны любы лік<a href="#cite_note-48">[47]</a><a href="#cite_note-49">[48]</a><a href="#cite_note-50">[49]</a>.</blockquote> Тут Леанарда Пізанскі піша "знак 0" маючы на ўвазе што ён падобны да знакаў арыфметычных дзеянняў, такіх як складанне і множанне. З XIII ст. у Еўропе становяцца папулярнымі падручнікі па лічэнні (складанне, множанне, караняванне і інш.), якія называліся <a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B0%D1%80%D1%8B%D0%B7%D0%BC&action=edit&redlink=1" class="new" title="Алгарызм (няма такой старонкі)">алгарызмамі</a><a href="https://en.wikipedia.org/wiki/Algorism" class="extiw" title="en:Algorism">[en]</a> паводле персідскага матэматыка <a href="/wiki/%D0%9C%D1%83%D1%85%D0%B0%D0%BC%D0%B0%D0%B4_%D0%90%D0%BB%D1%8C-%D0%A5%D0%B0%D1%80%D1%8D%D0%B7%D0%BC%D1%96" title="Мухамад Аль-Харэзмі">Аль-Харэзмі</a>. Найвядомейшы падручнік быў напісаны <a href="/w/index.php?title=%D0%86%D0%B0%D0%B3%D0%B0%D0%BD_%D0%B4%D1%8D_%D0%A1%D0%B0%D0%BA%D1%80%D0%B0%D0%B1%D0%BE%D1%81%D0%BA%D0%B0&action=edit&redlink=1" class="new" title="Іаган дэ Сакрабоска (няма такой старонкі)">Іаганам дэ Сакрабоска</a><a href="https://en.wikipedia.org/wiki/Johannes_de_Sacrobosco" class="extiw" title="en:Johannes de Sacrobosco">[en]</a> каля 1235 г. і ў 1488 г. стаў адной з першых надрукаваных навуковых кніг. Да канца XV-га стагоддзя сярод матэматыкаў, падобна, пераважалі інда-арабскія лічбы, у той час як гандляры аддавалі перавагу <a href="/wiki/%D0%A0%D1%8B%D0%BC%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Рымская сістэма злічэння">рымскім</a>. У XVI стагоддзі арабскія лічбы сталі шырока ўжывацца ў Еўропе. У Еўропе доўгі час нуль лічыўся ўмоўным знакам і не прызнаваўся лікам. Нават у XVII стагоддзі <a href="/wiki/%D0%94%D0%B6%D0%BE%D0%BD_%D0%92%D0%B0%D0%BB%D1%96%D1%81" title="Джон Валіс">Валіс</a> пісаў: «Нуль не ёсць лік». У арыфметычных працах адмоўны лік тлумачыўся як доўг, а нуль — як сітуацыя поўнага спусташэння. Поўнаму ўраўнаванню яго ў правах з іншымі лікамі асабліва спрыялі працы <a href="/wiki/%D0%9B%D0%B5%D0%B0%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леанард Эйлер">Леанарда Эйлера</a>. <div class="mw-heading mw-heading2"><h2 id="Гл._таксама">Гл. таксама</h2>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=17" title="Правіць раздзел: Гл. таксама" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=17" title="Правіць зыходнік раздзела: Гл. таксама">правіць зыходнік</a>]</div> <ul><li><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D0%BE%D1%9E%D0%BD%D1%8B_%D1%96_%D0%B4%D0%B0%D0%B4%D0%B0%D1%82%D0%BD%D1%8B_%D0%BD%D1%83%D0%BB%D1%8C&action=edit&redlink=1" class="new" title="Адмоўны і дадатны нуль (няма такой старонкі)">-0 і +0</a> — фіктыўныя паняцці ў <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Матэматычны аналіз">матэматычным аналізе</a>.</li> <li><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D1%8B%D0%BD%D0%BD%D1%8B_%D0%BD%D1%83%D0%BB%D1%8C&action=edit&redlink=1" class="new" title="Машынны нуль (няма такой старонкі)">Машынны нуль</a></li> <li><a href="/w/index.php?title=%D0%9D%D1%83%D0%BB%D1%8C,_%D0%BB%D1%96%D1%87%D0%B1%D0%B0&action=edit&redlink=1" class="new" title="Нуль, лічба (няма такой старонкі)">Лічба 0</a></li> <li><a href="/wiki/%D0%90%D0%B4%D0%BC%D0%BE%D1%9E%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Адмоўны лік">Адмоўны лік</a></li> <li><a href="/w/index.php?title=%D0%94%D0%B7%D0%B5%D0%BB%D1%8C%D0%BD%D1%96%D0%BA_%D0%BD%D1%83%D0%BB%D1%8F&action=edit&redlink=1" class="new" title="Дзельнік нуля (няма такой старонкі)">Дзельнік нуля</a></li> <li><a href="/wiki/1_(%D0%BB%D1%96%D0%BA)" title="1 (лік)">Лік 1</a> — <a href="/w/index.php?title=%D0%9D%D0%B5%D0%B9%D1%82%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82&action=edit&redlink=1" class="new" title="Нейтральны элемент (няма такой старонкі)">мультыплікатыўная адзінка</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Заўвагі">Заўвагі</h2>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=18" title="Правіць раздзел: Заўвагі" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=18" title="Правіць зыходнік раздзела: Заўвагі">правіць зыходнік</a>]</div> <div class="reflist columns" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-7"><a href="#cite_ref-7">↑</a> Да 3-га стагоддзя нашай эры не было знойдзена ніводнай даты доўгага падліку з выкарыстаннем лічбы 0, але праз тое, што сістэма доўгага падліку не мела б сэнсу без нейкага запаўняльніка і тое, што мезаамерыканскія гліфы звычайна не пакідалі пустых месцаў, гэтыя больш раннія даты ўважаюцца ўскоснымі доказамі таго, што канцэпцыя нуля ўжо існавала ў той час. </li> </ol></div> </div> <div class="mw-heading mw-heading2"><h2 id="Зноскі">Зноскі</h2>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=19" title="Правіць раздзел: Зноскі" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=19" title="Правіць зыходнік раздзела: Зноскі">правіць зыходнік</a>]</div> <div class="reflist columns" style="list-style-type: decimal;"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">↑</a> <style data-mw-deduplicate="TemplateStyles:r4817788">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a{background-size:contain}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a{background-size:contain}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a{background-size:contain}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#2C882D;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911F}html.skin-theme-clientpref-night .mw-parser-output .cs1-visible-error,html.skin-theme-clientpref-night .mw-parser-output .cs1-hidden-error{color:#f8a397}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-visible-error,html.skin-theme-clientpref-os .mw-parser-output .cs1-hidden-error{color:#f8a397}html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911F}}</style><cite id="CITEREFBuntJonesBedient1976" class="citation book cs1">Bunt, Lucas Nicolaas Hendrik; Jones, Phillip S.; Bedient, Jack D. (1976). <a rel="nofollow" class="external text" href="http://books.google.com/books?id=7xArILpcndYC">The historical roots of elementary mathematics</a>. Courier Dover Publications. pp. 254–255. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/0-486-13968-9" title="Адмысловае:BookSources/0-486-13968-9"><bdi>0-486-13968-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+historical+roots+of+elementary+mathematics&rft.pages=254-255&rft.pub=Courier+Dover+Publications&rft.date=1976&rft.isbn=0-486-13968-9&rft.aulast=Bunt&rft.aufirst=Lucas+Nicolaas+Hendrik&rft.au=Jones%2C+Phillip+S.&rft.au=Bedient%2C+Jack+D.&rft_id=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7xArILpcndYC&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988">, <a rel="nofollow" class="external text" href="http://books.google.com/books?id=7xArILpcndYC&pg=PA255">Extract of pages 254—255</a> </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> <a rel="nofollow" class="external text" href="http://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html">Egyptian numerals</a> (нявызн.). <a href="/w/index.php?title=Mathshistory.st-andrews.ac.uk&action=edit&redlink=1" class="new" title="Mathshistory.st-andrews.ac.uk (няма такой старонкі)">mathshistory.st-andrews.ac.uk</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20191115221313/http://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html">Архівавана</a> з першакрыніцы 15 November 2019. Праверана 21 December 2019. </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFJoseph2011" class="citation book cs1">Joseph, George Gheverghese (2011). <a rel="nofollow" class="external text" href="https://archive.org/details/crestpeacocknone00jose">The Crest of the Peacock: Non-European Roots of Mathematics</a> (Third ed.). Princeton UP. p. <a rel="nofollow" class="external text" href="https://archive.org/details/crestpeacocknone00jose/page/n116">86</a>. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-691-13526-7" title="Адмысловае:BookSources/978-0-691-13526-7"><bdi>978-0-691-13526-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Crest+of+the+Peacock%3A+Non-European+Roots+of+Mathematics&rft.pages=86&rft.edition=Third&rft.pub=Princeton+UP&rft.date=2011&rft.isbn=978-0-691-13526-7&rft.aulast=Joseph&rft.aufirst=George+Gheverghese&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcrestpeacocknone00jose&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-multiref1-4"><a href="#cite_ref-multiref1_4-0">↑</a> Kaplan, Robert. (2000). The Nothing That Is: A Natural History of Zero. Oxford: Oxford University Press. </li> <li id="cite_note-5"><a href="#cite_ref-5">↑</a> <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/">Zero</a> (англ.). Maths History. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210921191118/https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/">Архівавана</a> з першакрыніцы 21 September 2021. Праверана 7 верасня 2021. </li> <li id="cite_note-6"><a href="#cite_ref-6">↑</a> <a rel="nofollow" class="external text" href="https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?printable=1&id=1976">Babylonian mathematics: View as single page</a> (нявызн.). www.open.edu. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210907135356/https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?printable=1&id=1976">Архівавана</a> з першакрыніцы 7 September 2021. Праверана 7 верасня 2021. </li> <li id="cite_note-8"><a href="#cite_ref-8">↑</a> Diehl, p. 186 </li> <li id="cite_note-9"><a href="#cite_ref-9">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFMortaigne2014" class="citation news cs1">Mortaigne, Véronique (28 November 2014). <a rel="nofollow" class="external text" href="https://www.theguardian.com/culture/2014/nov/28/mayan-civilisation-paris-exhibition">"The golden age of Mayan civilisation – exhibition review"</a>. <a href="/wiki/The_Guardian" title="The Guardian">The Guardian</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141128222215/http://www.theguardian.com/culture/2014/nov/28/mayan-civilisation-paris-exhibition">Архівавана</a> з арыгінала 28 November 2014. Праверана 10 October 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Guardian&rft.atitle=The+golden+age+of+Mayan+civilisation+%E2%80%93+exhibition+review&rft.date=2014-11-28&rft.aulast=Mortaigne&rft.aufirst=V%C3%A9ronique&rft_id=https%3A%2F%2Fwww.theguardian.com%2Fculture%2F2014%2Fnov%2F28%2Fmayan-civilisation-paris-exhibition&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-10"><a href="#cite_ref-10">↑</a> Wallin, Nils-Bertil. <a rel="nofollow" class="external text" href="http://yaleglobal.yale.edu/about/zero.jsp">The History of Zero</a> (нявызн.)(недаступная спасылка). YaleGlobal online. The Whitney and Betty Macmillan Center for International and Area Studies at Yale. (19 лістапада 2002). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160825124525/http://yaleglobal.yale.edu/about/zero.jsp">Архівавана</a> з першакрыніцы 25 August 2016. Праверана 1 September 2016. </li> <li id="cite_note-Seife2000-11">↑ <a href="#cite_ref-Seife2000_11-0">а</a> <a href="#cite_ref-Seife2000_11-1">б</a> <a href="#cite_ref-Seife2000_11-2">в</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFSeife2000" class="citation book cs1">Seife, Charles (1 September 2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=obJ70nxVYFUC">Zero: The Biography of a Dangerous Idea</a>. Penguin. p. 39. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-14-029647-1" title="Адмысловае:BookSources/978-0-14-029647-1"><bdi>978-0-14-029647-1</bdi></a>. <a href="/w/index.php?title=OCLC_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)&action=edit&redlink=1" class="new" title="OCLC (ідэнтыфікатар) (няма такой старонкі)">OCLC</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/1005913932">1005913932</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220430084920/https://books.google.com/books?id=obJ70nxVYFUC">Архівавана</a> з арыгінала 30 April 2022. Праверана 30 April 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Zero%3A+The+Biography+of+a+Dangerous+Idea&rft.pages=39&rft.pub=Penguin&rft.date=2000-09-01&rft_id=info%3Aoclcnum%2F1005913932&rft.isbn=978-0-14-029647-1&rft.aulast=Seife&rft.aufirst=Charles&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DobJ70nxVYFUC&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-Nieder2019-12"><a href="#cite_ref-Nieder2019_12-0">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFNieder2019" class="citation book cs1">Nieder, Andreas (19 November 2019). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=x4y5DwAAQBAJ&pg=PA286">A Brain for Numbers: The Biology of the Number Instinct</a>. MIT Press. p. 286. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-262-35432-5" title="Адмысловае:BookSources/978-0-262-35432-5"><bdi>978-0-262-35432-5</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220430093316/https://books.google.com/books?id=x4y5DwAAQBAJ&pg=PA286">Архівавана</a> з арыгінала 30 April 2022. Праверана 30 April 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Brain+for+Numbers%3A+The+Biology+of+the+Number+Instinct&rft.pages=286&rft.pub=MIT+Press&rft.date=2019-11-19&rft.isbn=978-0-262-35432-5&rft.aulast=Nieder&rft.aufirst=Andreas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dx4y5DwAAQBAJ%26pg%3DPA286&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-Kaplan1999-13"><a href="#cite_ref-Kaplan1999_13-0">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFKaplan1999" class="citation book cs1">Kaplan, Robert (28 October 1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Bn0EBVsfi1YC">The Nothing that Is: A Natural History of Zero</a>. Oxford University Press. p. 17. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-19-802945-8" title="Адмысловае:BookSources/978-0-19-802945-8"><bdi>978-0-19-802945-8</bdi></a>. <a href="/w/index.php?title=OCLC_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)&action=edit&redlink=1" class="new" title="OCLC (ідэнтыфікатар) (няма такой старонкі)">OCLC</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/466431211">466431211</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140624063502/http://books.google.com/books?id=Bn0EBVsfi1YC">Архівавана</a> з арыгінала 24 June 2014. Праверана 30 April 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Nothing+that+Is%3A+A+Natural+History+of+Zero&rft.pages=17&rft.pub=Oxford+University+Press&rft.date=1999-10-28&rft_id=info%3Aoclcnum%2F466431211&rft.isbn=978-0-19-802945-8&rft.aulast=Kaplan&rft.aufirst=Robert&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBn0EBVsfi1YC&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-14"><a href="#cite_ref-14">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFHuggett2019" class="citation encyclopaedia cs1">Huggett, Nick (2019). <a rel="nofollow" class="external text" href="https://plato.stanford.edu/archives/win2019/entries/paradox-zeno/">"Zeno's Paradoxes"</a>. In Zalta, Edward N. (рэд.). The Stanford Encyclopedia of Philosophy (Winter 2019 ed.). Metaphysics Research Lab, Stanford University. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210110135804/https://plato.stanford.edu/archives/win2019/entries/paradox-zeno/">Архівавана</a> з арыгінала 10 January 2021. Праверана 2020-08-09.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Zeno%27s+Paradoxes&rft.btitle=The+Stanford+Encyclopedia+of+Philosophy&rft.edition=Winter+2019&rft.pub=Metaphysics+Research+Lab%2C+Stanford+University&rft.date=2019&rft.aulast=Huggett&rft.aufirst=Nick&rft_id=https%3A%2F%2Fplato.stanford.edu%2Farchives%2Fwin2019%2Fentries%2Fparadox-zeno%2F&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-15"><a href="#cite_ref-15">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFNeugebauer1969" class="citation book cs1"><a href="/w/index.php?title=Otto_E._Neugebauer&action=edit&redlink=1" class="new" title="Otto E. Neugebauer (няма такой старонкі)">Neugebauer, Otto</a> (1969) [1957]. <a rel="nofollow" class="external text" href="https://archive.org/details/exactsciencesant00neug">The Exact Sciences in Antiquity</a>. Vol. 9 (2 ed.). <a href="/w/index.php?title=Dover_Publications&action=edit&redlink=1" class="new" title="Dover Publications (няма такой старонкі)">Dover Publications</a>. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/exactsciencesant00neug/page/n30">13</a>–14, plate 2. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-486-22332-2" title="Адмысловае:BookSources/978-0-486-22332-2"><bdi>978-0-486-22332-2</bdi></a>. <a href="/wiki/PMID_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="PMID (ідэнтыфікатар)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/14884919">14884919</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Exact+Sciences+in+Antiquity&rft.pages=13-14%2C+plate+2&rft.edition=2&rft.pub=Dover+Publications&rft.date=1969&rft_id=info%3Apmid%2F14884919&rft.isbn=978-0-486-22332-2&rft.aulast=Neugebauer&rft.aufirst=Otto&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fexactsciencesant00neug&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> <code class="cs1-code">{{<a href="/wiki/%D0%A8%D0%B0%D0%B1%D0%BB%D0%BE%D0%BD:Cite_book" title="Шаблон:Cite book">cite book</a>}}</code>: <code class="cs1-code">|journal=</code> ігнараваны (<a href="/w/index.php?title=%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%9F%D0%B0%D0%BC%D1%8B%D0%BB%D0%BA%D1%96_%D1%88%D0%B0%D0%B1%D0%BB%D0%BE%D0%BD%D0%B0%D1%9E_CS1/2&action=edit&redlink=1" class="new" title="Вікіпедыя:Памылкі шаблонаў CS1/2 (няма такой старонкі)">даведка</a>) </li> <li id="cite_note-Mercier-16"><a href="#cite_ref-Mercier_16-0">↑</a> Mercier, Raymond. <a rel="nofollow" class="external text" href="http://www.raymondm.co.uk/prog/GreekZeroSign.pdf">Consideration of the Greek symbol 'zero'</a> (нявызн.). Home of Kairos. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201105113109/http://www.raymondm.co.uk/prog/GreekZeroSign.pdf">Архівавана</a> з першакрыніцы 5 November 2020. Праверана 28 March 2020. </li> <li id="cite_note-Ptolemy-17"><a href="#cite_ref-Ptolemy_17-0">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFPtolemy1998" class="citation book cs1"><a href="/w/index.php?title=Ptolemy&action=edit&redlink=1" class="new" title="Ptolemy (няма такой старонкі)">Ptolemy</a> (1998) [1984, каля 150]. Ptolemy's Almagest. Перакладчык <a href="/w/index.php?title=Gerald_J._Toomer&action=edit&redlink=1" class="new" title="Gerald J. Toomer (няма такой старонкі)">Toomer, G. J.</a> <a href="/w/index.php?title=Princeton_University_Press&action=edit&redlink=1" class="new" title="Princeton University Press (няма такой старонкі)">Princeton University Press</a>. pp. 306–307. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/0-691-00260-6" title="Адмысловае:BookSources/0-691-00260-6"><bdi>0-691-00260-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ptolemy%27s+Almagest&rft.pages=306-307&rft.pub=Princeton+University+Press&rft.date=1998&rft.isbn=0-691-00260-6&rft.au=Ptolemy&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-18"><a href="#cite_ref-18">↑</a> <a rel="nofollow" class="external text" href="http://mathshistory.st-andrews.ac.uk/HistTopics/Zero.html">A history of Zero</a> (нявызн.). MacTutor History of Mathematics. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200407074239/http://mathshistory.st-andrews.ac.uk/HistTopics/Zero.html">Архівавана</a> з першакрыніцы 7 April 2020. Праверана 28 March 2020. </li> <li id="cite_note-Neugebauer-19"><a href="#cite_ref-Neugebauer_19-0">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFNeugebauer2016" class="citation book cs1"><a href="/w/index.php?title=Otto_Neugebauer&action=edit&redlink=1" class="new" title="Otto Neugebauer (няма такой старонкі)">Neugebauer, Otto</a> (2016) [1979]. Ethiopic Astronomy and Computus (Red Sea Press ed.). Red Sea Press. pp. 25, 53, 93, 183, Plate I. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-1-56902-440-9" title="Адмысловае:BookSources/978-1-56902-440-9"><bdi>978-1-56902-440-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ethiopic+Astronomy+and+Computus&rft.pages=25%2C+53%2C+93%2C+183%2C+Plate+I&rft.edition=Red+Sea+Press&rft.pub=Red+Sea+Press&rft.date=2016&rft.isbn=978-1-56902-440-9&rft.aulast=Neugebauer&rft.aufirst=Otto&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988">. The pages in this edition have numbers six less than the same pages in the original edition. </li> <li id="cite_note-Dionysius-20"><a href="#cite_ref-Dionysius_20-0">↑</a> Deckers, Michael. <a rel="nofollow" class="external text" href="http://hbar.phys.msu.ru/gorm/chrono/paschata.htm">Cyclus Decemnovennalis Dionysii – Nineteen Year Cycle of Dionysius</a> (нявызн.) (2003). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190115083618/http://hbar.phys.msu.ru/gorm/chrono/paschata.htm">Архівавана</a> з першакрыніцы 15 January 2019. </li> <li id="cite_note-zero-21"><a href="#cite_ref-zero_21-0">↑</a> C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina. </li> <li id="cite_note-Hodgkin-22">↑ <a href="#cite_ref-Hodgkin_22-0">а</a> <a href="#cite_ref-Hodgkin_22-1">б</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFHodgkin2005" class="citation book cs1">Hodgkin, Luke (2005). <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema0000hodg">A History of Mathematics : From Mesopotamia to Modernity: From Mesopotamia to Modernity</a>. Oxford University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema0000hodg/page/85">85</a>. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-19-152383-0" title="Адмысловае:BookSources/978-0-19-152383-0"><bdi>978-0-19-152383-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Mathematics+%3A+From+Mesopotamia+to+Modernity%3A+From+Mesopotamia+to+Modernity&rft.pages=85&rft.pub=Oxford+University+Press&rft.date=2005&rft.isbn=978-0-19-152383-0&rft.aulast=Hodgkin&rft.aufirst=Luke&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofmathema0000hodg&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-23"><a href="#cite_ref-23">↑</a> O'Connor, J.J.. <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/HistTopics/Chinese_numerals/">Chinese numerals</a> (нявызн.). Mac Tutor. School of Mathematics and Statistics University of St Andrews, Scotland (1 студзеня 2004). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200614115729/https://mathshistory.st-andrews.ac.uk/HistTopics/Chinese_numerals/">Архівавана</a> з першакрыніцы 14 June 2020. Праверана 14 June 2020. </li> <li id="cite_note-24"><a href="#cite_ref-24">↑</a> Crossley, Lun. 1999, p. 12 «the ancient Chinese system is a place notation system» </li> <li id="cite_note-Crossley-25"><a href="#cite_ref-Crossley_25-0">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFKang-Shen_ShenJohn_N._CrossleyAnthony_W.C._LunHui_Liu1999" class="citation book cs1">Kang-Shen Shen; John N. Crossley; Anthony W.C. Lun; Hui Liu (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=eiTJHRGTG6YC3">The Nine Chapters on the Mathematical Art: Companion and Commentary</a>. Oxford UP. p. 35. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-19-853936-0" title="Адмысловае:BookSources/978-0-19-853936-0"><bdi>978-0-19-853936-0</bdi></a>. <q>zero was regarded as a number in India ... whereas the Chinese employed a vacant position</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Nine+Chapters+on+the+Mathematical+Art%3A+Companion+and+Commentary&rft.pages=35&rft.pub=Oxford+UP&rft.date=1999&rft.isbn=978-0-19-853936-0&rft.au=Kang-Shen+Shen&rft.au=John+N.+Crossley&rft.au=Anthony+W.C.+Lun&rft.au=Hui+Liu&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DeiTJHRGTG6YC3&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-Qin-26"><a href="#cite_ref-Qin_26-0">↑</a> <a rel="nofollow" class="external text" href="http://grmath4.phpnet.us/istoria/the_history_of%20math_greece/the_history_of%20math_greece_3-5.pdf">Mathematics in the Near and Far East</a> (нявызн.). grmath4.phpnet.us. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131104120005/http://grmath4.phpnet.us/istoria/the_history_of%20math_greece/the_history_of%20math_greece_3-5.pdf">Архівавана</a> з першакрыніцы 10 August 2018. Праверана 7 June 2012. </li> <li id="cite_note-struik33-27"><a href="#cite_ref-struik33_27-0">↑</a> Struik, Dirk J. (1987). A Concise History of Mathematics. New York: Dover Publications. pp. 32-33. «In these matrices we find negative numbers, which appear here for the first time in history.» </li> <li id="cite_note-plofker-28">↑ <a href="#cite_ref-plofker_28-0">а</a> <a href="#cite_ref-plofker_28-1">б</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFPlofker2009" class="citation book cs1"><a href="/w/index.php?title=Kim_Plofker&action=edit&redlink=1" class="new" title="Kim Plofker (няма такой старонкі)">Plofker, Kim</a> (2009). <a href="/w/index.php?title=Mathematics_in_India_(book)&action=edit&redlink=1" class="new" title="Mathematics in India (book) (няма такой старонкі)">Mathematics in India</a>. Princeton University Press. pp. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DHvThPNp9yMC&pg=PA54">54–56</a>. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-691-12067-6" title="Адмысловае:BookSources/978-0-691-12067-6"><bdi>978-0-691-12067-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+in+India&rft.pages=54-56&rft.pub=Princeton+University+Press&rft.date=2009&rft.isbn=978-0-691-12067-6&rft.aulast=Plofker&rft.aufirst=Kim&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-29"><a href="#cite_ref-29">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFVaman_Shivaram_Apte1970" class="citation book cs1">Vaman Shivaram Apte (1970). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=4ArxvCxV1l4C&pg=PA648">Sanskrit Prosody and Important Literary and Geographical Names in the Ancient History of India</a>. Motilal Banarsidass. pp. 648–649. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-81-208-0045-8" title="Адмысловае:BookSources/978-81-208-0045-8"><bdi>978-81-208-0045-8</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170422124355/https://books.google.com/books?id=4ArxvCxV1l4C&pg=PA648">Архівавана</a> з арыгінала 22 April 2017. Праверана 21 April 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sanskrit+Prosody+and+Important+Literary+and+Geographical+Names+in+the+Ancient+History+of+India&rft.pages=648-649&rft.pub=Motilal+Banarsidass&rft.date=1970&rft.isbn=978-81-208-0045-8&rft.au=Vaman+Shivaram+Apte&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D4ArxvCxV1l4C%26pg%3DPA648&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-30"><a href="#cite_ref-30">↑</a> <a rel="nofollow" class="external text" href="http://people.sju.edu/~rhall/Rhythms/Poets/arcadia.pdf">Math for Poets and Drummers</a> (нявызн.)(недаступная спасылка). people.sju.edu. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190122014628/http://people.sju.edu/~rhall/Rhythms/Poets/arcadia.pdf">Архівавана</a> з першакрыніцы 22 January 2019. Праверана 20 December 2015. </li> <li id="cite_note-bourbaki46-31"><a href="#cite_ref-bourbaki46_31-0">↑</a> Bourbaki, Nicolas Elements of the History of Mathematics (1998), p. 46 </li> <li id="cite_note-Weiss-32"><a href="#cite_ref-Weiss_32-0">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFWeiss2017" class="citation news cs1">Weiss, Ittay (20 September 2017). <a rel="nofollow" class="external text" href="https://theconversation.com/nothing-matters-how-the-invention-of-zero-helped-create-modern-mathematics-84232">"Nothing matters: How India's invention of zero helped create modern mathematics"</a>. The Conversation. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180712124031/https://theconversation.com/nothing-matters-how-the-invention-of-zero-helped-create-modern-mathematics-84232">Архівавана</a> з арыгінала 12 July 2018. Праверана 12 July 2018.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Conversation&rft.atitle=Nothing+matters%3A+How+India%27s+invention+of+zero+helped+create+modern+mathematics&rft.date=2017-09-20&rft.aulast=Weiss&rft.aufirst=Ittay&rft_id=https%3A%2F%2Ftheconversation.com%2Fnothing-matters-how-the-invention-of-zero-helped-create-modern-mathematics-84232&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-33"><a href="#cite_ref-33">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFDevlin2017" class="citation news cs1">Devlin, Hannah (13 September 2017). <a rel="nofollow" class="external text" href="https://www.theguardian.com/science/2017/sep/14/much-ado-about-nothing-ancient-indian-text-contains-earliest-zero-symbol">"Much ado about nothing: ancient Indian text contains earliest zero symbol"</a>. The Guardian. <a href="/wiki/ISSN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISSN (ідэнтыфікатар)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/0261-3077">0261-3077</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171120225416/https://www.theguardian.com/science/2017/sep/14/much-ado-about-nothing-ancient-indian-text-contains-earliest-zero-symbol">Архівавана</a> з арыгінала 20 November 2017. Праверана 14 September 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Guardian&rft.atitle=Much+ado+about+nothing%3A+ancient+Indian+text+contains+earliest+zero+symbol&rft.date=2017-09-13&rft.issn=0261-3077&rft.aulast=Devlin&rft.aufirst=Hannah&rft_id=https%3A%2F%2Fwww.theguardian.com%2Fscience%2F2017%2Fsep%2F14%2Fmuch-ado-about-nothing-ancient-indian-text-contains-earliest-zero-symbol&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-34"><a href="#cite_ref-34">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFRevell2017" class="citation news cs1">Revell, Timothy (14 September 2017). <a rel="nofollow" class="external text" href="https://www.newscientist.com/article/2147450-history-of-zero-pushed-back-500-years-by-ancient-indian-text">"History of zero pushed back 500 years by ancient Indian text"</a>. New Scientist. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171025185119/https://www.newscientist.com/article/2147450-history-of-zero-pushed-back-500-years-by-ancient-indian-text">Архівавана</a> з арыгінала 25 October 2017. Праверана 25 October 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+Scientist&rft.atitle=History+of+zero+pushed+back+500+years+by+ancient+Indian+text&rft.date=2017-09-14&rft.aulast=Revell&rft.aufirst=Timothy&rft_id=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2147450-history-of-zero-pushed-back-500-years-by-ancient-indian-text&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-35"><a href="#cite_ref-35">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://www.bodleian.ox.ac.uk/bodley/news/2017/sep-14">"Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'"</a>. Bodleian Library. 14 September 2017. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170914215604/http://www.bodleian.ox.ac.uk/bodley/news/2017/sep-14">Архівавана</a> з арыгінала 14 September 2017. Праверана 25 October 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bodleian+Library&rft.atitle=Carbon+dating+finds+Bakhshali+manuscript+contains+oldest+recorded+origins+of+the+symbol+%27zero%27&rft.date=2017-09-14&rft_id=http%3A%2F%2Fwww.bodleian.ox.ac.uk%2Fbodley%2Fnews%2F2017%2Fsep-14&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-36"><a href="#cite_ref-36">↑</a> Ifrah, Georges (2000), p. 416. </li> <li id="cite_note-Aryab-37"><a href="#cite_ref-Aryab_37-0">↑</a> Aryabhatiya of Aryabhata, translated by <a href="/w/index.php?title=Walter_Eugene_Clark&action=edit&redlink=1" class="new" title="Walter Eugene Clark (няма такой старонкі)">Walter Eugene Clark</a>. </li> <li id="cite_note-38"><a href="#cite_ref-38">↑</a> O'Connor, Robertson, J.J., E.F.. <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html">Aryabhata the Elder</a> (нявызн.). School of Mathematics and Statistics University of St Andrews, Scotland. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150711055702/http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html">Архівавана</a> з першакрыніцы 11 July 2015. Праверана 26 May 2013. </li> <li id="cite_note-39"><a href="#cite_ref-39">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFWilliam_L._Hosch2010" class="citation book cs1">William L. Hosch, рэд. (15 August 2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cuN7rH6RzikC&pg=PA97">The Britannica Guide to Numbers and Measurement (Math Explained)</a>. The Rosen Publishing Group. pp. 97–98. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-1-61530-108-9" title="Адмысловае:BookSources/978-1-61530-108-9"><bdi>978-1-61530-108-9</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160804025243/https://books.google.com/books?id=cuN7rH6RzikC&pg=PA97">Архівавана</a> з арыгінала 4 August 2016. Праверана 26 September 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Britannica+Guide+to+Numbers+and+Measurement+%28Math+Explained%29&rft.pages=97-98&rft.pub=The+Rosen+Publishing+Group&rft.date=2010-08-15&rft.isbn=978-1-61530-108-9&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DcuN7rH6RzikC%26pg%3DPA97&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-brahmagupta-40"><a href="#cite_ref-brahmagupta_40-0">↑</a> <a rel="nofollow" class="external text" href="https://archive.org/details/algebrawitharith00brahuoft">Algebra with Arithmetic of Brahmagupta and Bhaskara</a>, translated to English by Henry Thomas Colebrooke (1817) London </li> <li id="cite_note-Kaplan-41"><a href="#cite_ref-Kaplan_41-0">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFKaplan1999" class="citation book cs1">Kaplan, Robert (1999). <a rel="nofollow" class="external text" href="https://archive.org/details/nothingthatisnat00kapl">The Nothing That Is: A Natural History of Zero</a>. New York: Oxford University Press. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/nothingthatisnat00kapl/page/68">68–75</a>. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-19-514237-2" title="Адмысловае:BookSources/978-0-19-514237-2"><bdi>978-0-19-514237-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Nothing+That+Is%3A+A+Natural+History+of+Zero&rft.place=New+York&rft.pages=68-75&rft.pub=Oxford+University+Press&rft.date=1999&rft.isbn=978-0-19-514237-2&rft.aulast=Kaplan&rft.aufirst=Robert&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnothingthatisnat00kapl&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-42"><a href="#cite_ref-42">↑</a> <a href="/w/index.php?title=Bill_Casselman_(mathematician)&action=edit&redlink=1" class="new" title="Bill Casselman (mathematician) (няма такой старонкі)">Casselman, Bill</a>. <a rel="nofollow" class="external text" href="http://www.ams.org/samplings/feature-column/fcarc-india-zero">All for Nought</a> (нявызн.). ams.org. University of British Columbia), American Mathematical Society. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151206184352/http://www.ams.org/samplings/feature-column/fcarc-india-zero">Архівавана</a> з першакрыніцы 6 December 2015. Праверана 20 December 2015. </li> <li id="cite_note-43"><a href="#cite_ref-43">↑</a> Ifrah, Georges (2000), p. 400. </li> <li id="cite_note-44"><a href="#cite_ref-44">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFPannekoek1961" class="citation book cs1">Pannekoek, A. (1961). A History of Astronomy. George Allen & Unwin. p. 165.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Astronomy&rft.pages=165&rft.pub=George+Allen+%26+Unwin&rft.date=1961&rft.aulast=Pannekoek&rft.aufirst=A.&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-Durant-45">↑ <a href="#cite_ref-Durant_45-0">а</a> <a href="#cite_ref-Durant_45-1">б</a> <a href="#cite_ref-Durant_45-2">в</a> Will Durant (1950), The Story of Civilization, Volume 4, The Age of Faith: Constantine to Dante – A.D. 325–1300, Simon & Schuster, <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-9650007-5-8" title="Адмысловае:BookSources/978-0-9650007-5-8">ISBN 978-0-9650007-5-8</a>, p. 241, "The Arabic inheritance of science was overwhelmingly Greek, but Hindu influences ranked next. In 773, at Mansur's behest, translations were made of the Siddhantas – Indian astronomical treatises dating as far back as 425 BC; these versions may have the vehicle through which the "Arabic" numerals and the zero were brought from India into Islam. In 813, al-Khwarizmi used the Hindu numerals in his astronomical tables." </li> <li id="cite_note-46"><a href="#cite_ref-46">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFBrezina2006" class="citation book cs1">Brezina, Corona (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=955jPgAACAAJ">Al-Khwarizmi: The Inventor of Algebra</a>. The Rosen Publishing Group. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-1-4042-0513-0" title="Адмысловае:BookSources/978-1-4042-0513-0"><bdi>978-1-4042-0513-0</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200229035314/https://books.google.com/books?id=955jPgAACAAJ">Архівавана</a> з арыгінала 29 February 2020. Праверана 26 September 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Al-Khwarizmi%3A+The+Inventor+of+Algebra&rft.pub=The+Rosen+Publishing+Group&rft.date=2006&rft.isbn=978-1-4042-0513-0&rft.aulast=Brezina&rft.aufirst=Corona&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D955jPgAACAAJ&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> <li id="cite_note-47"><a href="#cite_ref-47">↑</a> Will Durant (1950), The Story of Civilization, Volume 4, The Age of Faith, Simon & Schuster, <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-9650007-5-8" title="Адмысловае:BookSources/978-0-9650007-5-8">ISBN 978-0-9650007-5-8</a>, p. 241, "In 976, Muhammad ibn Ahmad, in his Keys of the Sciences, remarked that if, in a calculation, no number appears in the place of tens, a little circle should be used "to keep the rows". This circle the Mosloems called ṣifr, "empty" whence our cipher." </li> <li id="cite_note-48"><a href="#cite_ref-48">↑</a> Sigler, L., Fibonacci's Liber Abaci. English translation, Springer, 2003. </li> <li id="cite_note-49"><a href="#cite_ref-49">↑</a> Grimm, R.E., "The Autobiography of Leonardo Pisano", <a href="/w/index.php?title=Fibonacci_Quarterly&action=edit&redlink=1" class="new" title="Fibonacci Quarterly (няма такой старонкі)">Fibonacci Quarterly</a> 11/1 (February 1973), pp. 99–104. </li> <li id="cite_note-50"><a href="#cite_ref-50">↑</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4817788"><cite id="CITEREFHansen2008" class="citation book cs1">Hansen, Alice (2008-06-09). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=COJsbuUI1h8C&q=%22Therefore%2C+embracing+more+stringently+that+method+of+the+Hindus%2C+and+taking+stricter+pains+in+its+study%2C+while+adding+certain+things+from+my+own+understanding+and+inserting+also+certain+things+from+the+niceties+of+Euclid%27s+geometric+art.%22&pg=PT31">Primary Mathematics: Extending Knowledge in Practice</a>(англ.). SAGE. <a href="/wiki/ISBN_(%D1%96%D0%B4%D1%8D%D0%BD%D1%82%D1%8B%D1%84%D1%96%D0%BA%D0%B0%D1%82%D0%B0%D1%80)" class="mw-redirect" title="ISBN (ідэнтыфікатар)">ISBN</a> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:BookSources/978-0-85725-233-3" title="Адмысловае:BookSources/978-0-85725-233-3"><bdi>978-0-85725-233-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210307234959/https://books.google.com/books?id=COJsbuUI1h8C&q=%22Therefore%2C+embracing+more+stringently+that+method+of+the+Hindus%2C+and+taking+stricter+pains+in+its+study%2C+while+adding+certain+things+from+my+own+understanding+and+inserting+also+certain+things+from+the+niceties+of+Euclid%27s+geometric+art.%22&pg=PT31">Архівавана</a> з арыгінала 7 March 2021. Праверана 7 November 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Primary+Mathematics%3A+Extending+Knowledge+in+Practice&rft.pub=SAGE&rft.date=2008-06-09&rft.isbn=978-0-85725-233-3&rft.aulast=Hansen&rft.aufirst=Alice&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DCOJsbuUI1h8C%26q%3D%2522Therefore%252C%2Bembracing%2Bmore%2Bstringently%2Bthat%2Bmethod%2Bof%2Bthe%2BHindus%252C%2Band%2Btaking%2Bstricter%2Bpains%2Bin%2Bits%2Bstudy%252C%2Bwhile%2Badding%2Bcertain%2Bthings%2Bfrom%2Bmy%2Bown%2Bunderstanding%2Band%2Binserting%2Balso%2Bcertain%2Bthings%2Bfrom%2Bthe%2Bniceties%2Bof%2BEuclid%2527s%2Bgeometric%2Bart.%2522%26pg%3DPT31&rfr_id=info%3Asid%2Fbe.wikipedia.org%3A0+%28%D0%BB%D1%96%D0%BA%29" class="Z3988"> </li> </ol></div> </div> <div class="mw-heading mw-heading2"><h2 id="Спасылкі">Спасылкі</h2>[<a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&veaction=edit&section=20" title="Правіць раздзел: Спасылкі" class="mw-editsection-visualeditor">правіць</a> | <a href="/w/index.php?title=0_(%D0%BB%D1%96%D0%BA)&action=edit&section=20" title="Правіць зыходнік раздзела: Спасылкі">правіць зыходнік</a>]</div> <ul><li><a rel="nofollow" class="external text" href="http://shkolazhizni.ru/archive/0/n-38973/">История нуля</a></li> <li><a rel="nofollow" class="external text" href="http://www.vremia.ua/rubrics/khronograf/2902.php">Почему нельзя делить на ноль?</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150402191234/http://www.vremia.ua/rubrics/khronograf/2902.php">Архівавана</a> 2 красавіка 2015.</li> <li><a rel="nofollow" class="external text" href="http://www.ytime.com.ua/ru/24/347/0">Символика чисел (нуль)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150402102121/http://www.ytime.com.ua/ru/24/347/0">Архівавана</a> 2 красавіка 2015. /С. Курий/ «Время Z» № 2/2007</li> <li><a rel="nofollow" class="external text" href="http://library.mephi.ru/data/scientific-sessions/2003/6/046.html">О сопоставлении понятий «нуль» и «ничто»</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304103634/http://library.mephi.ru/data/scientific-sessions/2003/6/046.html">Архівавана</a> 4 сакавіка 2016. Смирнов О. А. — Научная сессия МИФИ-2003.</li> <li><a rel="nofollow" class="external text" href="http://bikubik.com/ru/?c=000000">Свойства числа ноль</a> (руск.)</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r4785216">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output 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старонкі)">Арыфметычныя</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1px">Рэчаісныя лікі і іх пашырэнні</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%D0%A0%D1%8D%D1%87%D0%B0%D1%96%D1%81%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Рэчаісны лік">Рэчаісныя</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {R} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac7df6838b44979c6531f6a0306206fbdb0477ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.187ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {R} }">)</li> <li><a href="/wiki/%D0%9A%D0%B0%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Камплексны лік">Камплексныя</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {C} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe3a54bb4e56c039e18c3af24ba70ab377f7a07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.187ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {C} }">)</li> <li><a href="/w/index.php?title=%D0%9A%D0%B2%D0%B0%D1%82%D1%8D%D1%80%D0%BD%D1%96%D1%91%D0%BD&action=edit&redlink=1" class="new" title="Кватэрніён (няма такой старонкі)">Кватэрніёны</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {H} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">H</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {H} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d00daea5df233d805f1ec5d5ae84845bac2ad06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.279ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {H} }">)</li> <li><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0_%D0%9A%D1%8D%D0%BB%D1%96&action=edit&redlink=1" class="new" title="Алгебра Кэлі (няма такой старонкі)">Лікі Кэлі (актавы, актаніёны)</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {O} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">O</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {O} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c5cf3960cf7ba384648447c15581d5d4589a6d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.279ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {O} }">)</li> <li><a href="/w/index.php?title=%D0%A1%D0%B5%D0%B4%D1%8D%D0%BD%D1%96%D1%91%D0%BD&action=edit&redlink=1" class="new" title="Седэніён (няма такой старонкі)">Седэніёны</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \mathbb {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">S</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \mathbb {S} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ef48a593f4503abeab608e8781ba478b7d1b304" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.914ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \mathbb {S} }">)</li> <li><a href="/w/index.php?title=%D0%90%D0%BB%D1%8C%D1%82%D1%8D%D1%80%D0%BD%D1%96%D1%91%D0%BD&action=edit&redlink=1" class="new" title="Альтэрніён (няма такой старонкі)">Альтэрніёны</a></li> <li><a href="/w/index.php?title=%D0%9F%D1%80%D0%B0%D1%86%D1%8D%D0%B4%D1%83%D1%80%D0%B0_%D0%9A%D1%8D%D0%BB%D1%96_%E2%80%94_%D0%94%D1%8B%D0%BA%D1%81%D0%B0%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Працэдура Кэлі — Дыксана (няма такой старонкі)">Працэдура Кэлі — Дыксана</a></li> <li><a href="/w/index.php?title=%D0%94%D1%83%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Дуальныя лікі (няма такой старонкі)">Дуальныя</a></li> <li><a href="/w/index.php?title=%D0%93%D1%96%D0%BF%D0%B5%D1%80%D0%BA%D0%B0%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&redlink=1" class="new" title="Гіперкамплексны лік (няма такой старонкі)">Гіперкамплексныя</a></li> <li><a href="/w/index.php?title=%D0%A1%D1%83%D0%BF%D0%B5%D1%80%D1%80%D1%8D%D1%87%D0%B0%D1%96%D1%81%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Суперрэчаісныя лікі (няма такой старонкі)">Суперрэчаісныя лікі</a> (<a href="https://en.wikipedia.org/wiki/Superreal_number" class="extiw" title="en:Superreal number">англ.</a>)</li> <li><a href="/w/index.php?title=%D0%93%D1%96%D0%BF%D0%B5%D1%80%D1%80%D1%8D%D1%87%D0%B0%D1%96%D1%81%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Гіперрэчаісныя лікі (няма такой старонкі)">Гіперрэчаісныя лікі</a> (<a href="https://en.wikipedia.org/wiki/Hyperreal_number" class="extiw" title="en:Hyperreal number">англ.</a>)</li> <li><a href="/w/index.php?title=%D0%A1%D1%8E%D1%80%D1%80%D1%8D%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Сюррэальныя лікі (няма такой старонкі)">Сюррэальныя лікі</a> (<a href="https://en.wikipedia.org/wiki/Surreal_number" class="extiw" title="en:Surreal number">англ.</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1px">Іншыя лікавыя сістэмы</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=%D0%9A%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="Кардынальны лік (няма такой старонкі)">Кардынальныя лікі</a></li> <li><a href="/w/index.php?title=%D0%9F%D0%B0%D1%80%D0%B0%D0%B4%D0%BA%D0%B0%D0%B2%D1%8B_%D0%BB%D1%96%D0%BA&action=edit&redlink=1" class="new" title="Парадкавы лік (няма такой старонкі)">Парадкавыя лікі (трансфінітныя, ардынал)</a></li> <li><a href="/wiki/P-%D0%B0%D0%B4%D1%8B%D1%87%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="P-адычны лік">p-адычныя</a></li> <li><a href="/w/index.php?title=%D0%A1%D1%83%D0%BF%D0%B5%D1%80%D0%BD%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&action=edit&redlink=1" class="new" title="Супернатуральныя лікі (няма такой старонкі)">Супернатуральныя лікі</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1px">Гл. таксама</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=%D0%9F%D0%B0%D0%B4%D0%B2%D0%BE%D0%B9%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Падвойныя лікі (няма такой старонкі)">Падвойныя лікі</a></li> <li><a href="/wiki/%D0%86%D1%80%D0%B0%D1%86%D1%8B%D1%8F%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Ірацыянальны лік">Ірацыянальныя лікі</a></li> <li><a href="/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%86%D1%8D%D0%BD%D0%B4%D1%8D%D0%BD%D1%82%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Трансцэндэнтны лік">Трансцэндэнтныя</a></li> <li><a href="/w/index.php?title=%D0%9B%D1%96%D0%BA%D0%B0%D0%B2%D1%8B_%D0%BF%D1%80%D0%B0%D0%BC%D0%B5%D0%BD%D1%8C&action=edit&redlink=1" class="new" title="Лікавы прамень (няма такой старонкі)">Лікавы прамень</a></li> <li><a href="/w/index.php?title=%D0%91%D1%96%D0%BA%D0%B2%D0%B0%D1%82%D1%8D%D1%80%D0%BD%D1%96%D1%91%D0%BD&action=edit&redlink=1" class="new" title="Бікватэрніён (няма такой старонкі)">Бікватэрніён</a></li></ul> </div></td></tr></tbody></table></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> 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