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mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E6%97%A0%E7%A9%B7" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <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="目录" 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">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</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">序言</div> </a> </li> <li id="toc-歷史" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#歷史"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>歷史</span> </div> </a> <button aria-controls="toc-歷史-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关歷史子章节</span> </button> <ul id="toc-歷史-sublist" class="vector-toc-list"> <li id="toc-早期無限的觀點" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#早期無限的觀點"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>早期無限的觀點</span> </div> </a> <ul id="toc-早期無限的觀點-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-文藝復興時代至近代" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#文藝復興時代至近代"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>文藝復興時代至近代</span> </div> </a> <ul id="toc-文藝復興時代至近代-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-數學中的無窮" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#數學中的無窮"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>數學中的無窮</span> </div> </a> <button aria-controls="toc-數學中的無窮-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关數學中的無窮子章节</span> </button> <ul id="toc-數學中的無窮-sublist" class="vector-toc-list"> <li id="toc-無限大的符號" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#無限大的符號"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>無限大的符號</span> </div> </a> <ul id="toc-無限大的符號-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-微積分及實分析中的無窮" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#微積分及實分析中的無窮"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>微積分及實分析中的無窮</span> </div> </a> <ul id="toc-微積分及實分析中的無窮-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-複變分析中的无穷" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#複變分析中的无穷"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>複變分析中的无穷</span> </div> </a> <ul id="toc-複變分析中的无穷-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-無窮大和無窮小" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#無窮大和無窮小"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>無窮大和無窮小</span> </div> </a> <ul id="toc-無窮大和無窮小-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-無窮遠點" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#無窮遠點"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>無窮遠點</span> </div> </a> <ul id="toc-無窮遠點-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-集合論中的無窮" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#集合論中的無窮"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>集合論中的無窮</span> </div> </a> <ul id="toc-集合論中的無窮-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-幾何學和拓扑学" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#幾何學和拓扑学"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>幾何學和拓扑学</span> </div> </a> <ul id="toc-幾何學和拓扑学-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-分形" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#分形"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.8</span> <span>分形</span> </div> </a> <ul id="toc-分形-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-沒有無窮的數學" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#沒有無窮的數學"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.9</span> <span>沒有無窮的數學</span> </div> </a> <ul id="toc-沒有無窮的數學-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-物理中的無窮" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#物理中的無窮"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>物理中的無窮</span> </div> </a> <ul id="toc-物理中的無窮-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-電腦計算中的無窮" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#電腦計算中的無窮"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>電腦計算中的無窮</span> </div> </a> <ul id="toc-電腦計算中的無窮-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-藝術及認知科學中的无穷" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#藝術及認知科學中的无穷"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>藝術及認知科學中的无穷</span> </div> </a> <ul id="toc-藝術及認知科學中的无穷-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-相關條目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#相關條目"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>相關條目</span> </div> </a> <ul id="toc-相關條目-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考資料" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考資料"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>參考資料</span> </div> </a> <ul id="toc-參考資料-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="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="目录" > <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="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">开关目录</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">无穷</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。114种语言可用" > <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-114" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">114种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Oneindigheid" title="Oneindigheid – 南非荷兰语" lang="af" hreflang="af" data-title="Oneindigheid" data-language-autonym="Afrikaans" data-language-local-name="南非荷兰语" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Unendlichkeit" title="Unendlichkeit – 瑞士德语" lang="gsw" hreflang="gsw" data-title="Unendlichkeit" data-language-autonym="Alemannisch" data-language-local-name="瑞士德语" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%8B%95%E1%88%8B%E1%8D%8D" title="አዕላፍ – 阿姆哈拉语" lang="am" hreflang="am" data-title="አዕላፍ" data-language-autonym="አማርኛ" data-language-local-name="阿姆哈拉语" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Infinito" title="Infinito – 阿拉贡语" lang="an" hreflang="an" data-title="Infinito" data-language-autonym="Aragonés" data-language-local-name="阿拉贡语" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%84%D8%A7%D9%86%D9%87%D8%A7%D9%8A%D8%A9" title="لانهاية – 阿拉伯语" lang="ar" hreflang="ar" data-title="لانهاية" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%84%D8%A7%D9%85%D8%B3%D8%A7%D9%84%D9%8A%D8%A9" title="لامسالية – 摩洛哥阿拉伯文" lang="ary" hreflang="ary" data-title="لامسالية" data-language-autonym="الدارجة" data-language-local-name="摩洛哥阿拉伯文" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D9%84%D9%87%D8%A7%D8%B4_%D9%86%D9%87%D8%A7%D9%8A%D9%87" title="ملهاش نهايه – 埃及阿拉伯文" lang="arz" hreflang="arz" data-title="ملهاش نهايه" data-language-autonym="مصرى" data-language-local-name="埃及阿拉伯文" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%85%E0%A6%B8%E0%A7%80%E0%A6%AE" title="অসীম – 阿萨姆语" lang="as" hreflang="as" data-title="অসীম" data-language-autonym="অসমীয়া" data-language-local-name="阿萨姆语" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Infinitu" title="Infinitu – 阿斯图里亚斯语" lang="ast" hreflang="ast" data-title="Infinitu" data-language-autonym="Asturianu" data-language-local-name="阿斯图里亚斯语" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sonsuzluq" title="Sonsuzluq – 阿塞拜疆语" lang="az" hreflang="az" data-title="Sonsuzluq" data-language-autonym="Azərbaycanca" data-language-local-name="阿塞拜疆语" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B3%D9%88%D9%86%D8%B3%D9%88%D8%B2" title="سونسوز – South Azerbaijani" lang="azb" hreflang="azb" data-title="سونسوز" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D0%B8%D0%BA%D2%BB%D0%B5%D2%99%D0%BB%D0%B5%D0%BA" title="Сикһеҙлек – 巴什基尔语" lang="ba" hreflang="ba" data-title="Сикһеҙлек" data-language-autonym="Башҡортса" data-language-local-name="巴什基尔语" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Begal%C4%ABb%C4%97" title="Begalībė – 薩莫吉希亞文" lang="sgs" hreflang="sgs" data-title="Begalībė" data-language-autonym="Žemaitėška" data-language-local-name="薩莫吉希亞文" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%B0%D0%BD%D0%B5%D1%87%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Бесканечнасць – 白俄罗斯语" lang="be" hreflang="be" data-title="Бесканечнасць" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%91%D1%8F%D1%81%D0%BA%D0%BE%D0%BD%D1%86%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Бясконцасьць – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Бясконцасьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B5%D0%B7%D0%BA%D1%80%D0%B0%D0%B9%D0%BD%D0%BE%D1%81%D1%82" title="Безкрайност – 保加利亚语" lang="bg" hreflang="bg" data-title="Безкрайност" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/Infinity" title="Infinity – 班亞爾文" lang="bjn" hreflang="bjn" data-title="Infinity" data-language-autonym="Banjar" data-language-local-name="班亞爾文" class="interlanguage-link-target"><span>Banjar</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%B8%E0%A7%80%E0%A6%AE" title="অসীম – 孟加拉语" lang="bn" hreflang="bn" data-title="অসীম" data-language-autonym="বাংলা" data-language-local-name="孟加拉语" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Beskona%C4%8Dnost" title="Beskonačnost – 波斯尼亚语" lang="bs" hreflang="bs" data-title="Beskonačnost" data-language-autonym="Bosanski" data-language-local-name="波斯尼亚语" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Infinit" title="Infinit – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Infinit" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%8E%DA%A9%DB%86%D8%AA%D8%A7%DB%8C%DB%8C" title="بێکۆتایی – 中库尔德语" lang="ckb" hreflang="ckb" data-title="بێکۆتایی" data-language-autonym="کوردی" data-language-local-name="中库尔德语" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Infinitu" title="Infinitu – 科西嘉语" lang="co" hreflang="co" data-title="Infinitu" data-language-autonym="Corsu" data-language-local-name="科西嘉语" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Nekone%C4%8Dno" title="Nekonečno – 捷克语" lang="cs" hreflang="cs" data-title="Nekonečno" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%92%C4%95%C3%A7%D1%81%C4%95%D1%80%D0%BB%C4%95%D1%85" title="Вĕçсĕрлĕх – 楚瓦什语" lang="cv" hreflang="cv" data-title="Вĕçсĕрлĕх" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什语" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Anfeidredd" title="Anfeidredd – 威尔士语" lang="cy" hreflang="cy" data-title="Anfeidredd" data-language-autonym="Cymraeg" data-language-local-name="威尔士语" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Uendelighed" title="Uendelighed – 丹麦语" lang="da" hreflang="da" data-title="Uendelighed" data-language-autonym="Dansk" data-language-local-name="丹麦语" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Unendlich_(Mathematik)" title="Unendlich (Mathematik) – 德语" lang="de" hreflang="de" data-title="Unendlich (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%86%CF%80%CE%B5%CE%B9%CF%81%CE%BF" title="Άπειρο – 希腊语" lang="el" hreflang="el" data-title="Άπειρο" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Infinity" title="Infinity – 英语" lang="en" hreflang="en" data-title="Infinity" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Senfineco" title="Senfineco – 世界语" lang="eo" hreflang="eo" data-title="Senfineco" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Infinito" title="Infinito – 西班牙语" lang="es" hreflang="es" data-title="Infinito" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/L%C3%B5pmatus" title="Lõpmatus – 爱沙尼亚语" lang="et" hreflang="et" data-title="Lõpmatus" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Infinitu" title="Infinitu – 巴斯克语" lang="eu" hreflang="eu" data-title="Infinitu" data-language-autonym="Euskara" data-language-local-name="巴斯克语" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%DB%8C%E2%80%8C%D9%86%D9%87%D8%A7%DB%8C%D8%AA" title="بی‌نهایت – 波斯语" lang="fa" hreflang="fa" data-title="بی‌نهایت" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/%C3%84%C3%A4rett%C3%B6myys" title="Äärettömyys – 芬兰语" lang="fi" hreflang="fi" data-title="Äärettömyys" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Infini" title="Infini – 法语" lang="fr" hreflang="fr" data-title="Infini" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/%C3%9Cnentelkhaid" title="Ünentelkhaid – 北弗里西亚语" lang="frr" hreflang="frr" data-title="Ünentelkhaid" data-language-autonym="Nordfriisk" data-language-local-name="北弗里西亚语" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/%C3%89igr%C3%ADoch" title="Éigríoch – 爱尔兰语" lang="ga" hreflang="ga" data-title="Éigríoch" data-language-autonym="Gaeilge" data-language-local-name="爱尔兰语" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%84%A1%E9%99%90" title="無限 – 赣语" lang="gan" hreflang="gan" data-title="無限" data-language-autonym="贛語" data-language-local-name="赣语" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Enfini" title="Enfini – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Enfini" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Infinito" title="Infinito – 加利西亚语" lang="gl" hreflang="gl" data-title="Infinito" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%85%E0%AA%A8%E0%AA%82%E0%AA%A4" title="અનંત – 古吉拉特语" lang="gu" hreflang="gu" data-title="અનંત" data-language-autonym="ગુજરાતી" data-language-local-name="古吉拉特语" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%99%D7%A0%D7%A1%D7%95%D7%A3" title="אינסוף – 希伯来语" lang="he" hreflang="he" data-title="אינסוף" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A4%82%E0%A4%A4" title="अनंत – 印地语" lang="hi" hreflang="hi" data-title="अनंत" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Anant" title="Anant – 斐濟印地文" lang="hif" hreflang="hif" data-title="Anant" data-language-autonym="Fiji Hindi" data-language-local-name="斐濟印地文" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Beskona%C4%8Dnost" title="Beskonačnost – 克罗地亚语" lang="hr" hreflang="hr" data-title="Beskonačnost" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/V%C3%A9gtelen" title="Végtelen – 匈牙利语" lang="hu" hreflang="hu" data-title="Végtelen" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B6%D5%BE%D5%A5%D6%80%D5%BB%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6_(%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1)" title="Անվերջություն (մաթեմատիկա) – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Անվերջություն (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Takhingga" title="Takhingga – 印度尼西亚语" lang="id" hreflang="id" data-title="Takhingga" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Awan_inggana" title="Awan inggana – 伊洛卡诺语" lang="ilo" hreflang="ilo" data-title="Awan inggana" data-language-autonym="Ilokano" data-language-local-name="伊洛卡诺语" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Infiniteso" title="Infiniteso – 伊多语" lang="io" hreflang="io" data-title="Infiniteso" data-language-autonym="Ido" data-language-local-name="伊多语" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%93endanleiki" title="Óendanleiki – 冰岛语" lang="is" hreflang="is" data-title="Óendanleiki" data-language-autonym="Íslenska" data-language-local-name="冰岛语" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Infinito_(matematica)" title="Infinito (matematica) – 意大利语" lang="it" hreflang="it" data-title="Infinito (matematica)" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%84%A1%E9%99%90" title="無限 – 日语" lang="ja" hreflang="ja" data-title="無限" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Infiniti" title="Infiniti – 牙買加克里奧爾英文" lang="jam" hreflang="jam" data-title="Infiniti" data-language-autonym="Patois" data-language-local-name="牙買加克里奧爾英文" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/li_ci%27i" title="li ci'i – 逻辑语" lang="jbo" hreflang="jbo" data-title="li ci'i" data-language-autonym="La .lojban." data-language-local-name="逻辑语" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A3%E1%83%A1%E1%83%90%E1%83%A1%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%9D%E1%83%91%E1%83%90" title="უსასრულობა – 格鲁吉亚语" lang="ka" hreflang="ka" data-title="უსასრულობა" data-language-autonym="ქართული" data-language-local-name="格鲁吉亚语" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A8%D0%B5%D0%BA%D1%81%D1%96%D0%B7%D0%B4%D1%96%D0%BA" title="Шексіздік – 哈萨克语" lang="kk" hreflang="kk" data-title="Шексіздік" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%A8%E0%B2%82%E0%B2%A4" title="ಅನಂತ – 卡纳达语" lang="kn" hreflang="kn" data-title="ಅನಂತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="卡纳达语" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AC%B4%ED%95%9C" title="무한 – 韩语" lang="ko" hreflang="ko" data-title="무한" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/B%C3%AAdaw%C3%AE" title="Bêdawî – 库尔德语" lang="ku" hreflang="ku" data-title="Bêdawî" data-language-autonym="Kurdî" data-language-local-name="库尔德语" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Didhiwedhter" title="Didhiwedhter – 康沃尔语" lang="kw" hreflang="kw" data-title="Didhiwedhter" data-language-autonym="Kernowek" data-language-local-name="康沃尔语" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A7%D0%B5%D0%BA%D1%81%D0%B8%D0%B7%D0%B4%D0%B8%D0%BA" title="Чексиздик – 柯尔克孜语" lang="ky" hreflang="ky" data-title="Чексиздик" data-language-autonym="Кыргызча" data-language-local-name="柯尔克孜语" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="典范条目"><a href="https://la.wikipedia.org/wiki/Infinitas" title="Infinitas – 拉丁语" lang="la" hreflang="la" data-title="Infinitas" data-language-autonym="Latina" data-language-local-name="拉丁语" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Begalyb%C4%97" title="Begalybė – 立陶宛语" lang="lt" hreflang="lt" data-title="Begalybė" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bezgal%C4%ABba" title="Bezgalība – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Bezgalība" data-language-autonym="Latviešu" data-language-local-name="拉脱维亚语" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tsiefa" title="Tsiefa – 马拉加斯语" lang="mg" hreflang="mg" data-title="Tsiefa" data-language-autonym="Malagasy" data-language-local-name="马拉加斯语" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Бесконечност – 马其顿语" lang="mk" hreflang="mk" data-title="Бесконечност" data-language-autonym="Македонски" data-language-local-name="马其顿语" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%A8%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%A4" title="അനന്തത – 马拉雅拉姆语" lang="ml" hreflang="ml" data-title="അനന്തത" data-language-autonym="മലയാളം" data-language-local-name="马拉雅拉姆语" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D1%8F%D0%B7%D0%B3%D0%B0%D0%B0%D1%80%D0%B3%D2%AF%D0%B9" title="Хязгааргүй – 蒙古语" lang="mn" hreflang="mn" data-title="Хязгааргүй" data-language-autonym="Монгол" data-language-local-name="蒙古语" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A4%82%E0%A4%A4" title="अनंत – 马拉地语" lang="mr" hreflang="mr" data-title="अनंत" data-language-autonym="मराठी" data-language-local-name="马拉地语" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ketakterhinggaan" title="Ketakterhinggaan – 马来语" lang="ms" hreflang="ms" data-title="Ketakterhinggaan" data-language-autonym="Bahasa Melayu" data-language-local-name="马来语" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%94%E1%80%94%E1%80%B9%E1%80%90" title="အနန္တ – 缅甸语" lang="my" hreflang="my" data-title="အနန္တ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="缅甸语" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Unendlichkeid" title="Unendlichkeid – 低地德语" lang="nds" hreflang="nds" data-title="Unendlichkeid" data-language-autonym="Plattdüütsch" data-language-local-name="低地德语" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Oneindigheid" title="Oneindigheid – 荷兰语" lang="nl" hreflang="nl" data-title="Oneindigheid" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Uendeleg" title="Uendeleg – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Uendeleg" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Uendelig" title="Uendelig – 书面挪威语" lang="nb" hreflang="nb" data-title="Uendelig" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Infinit" title="Infinit – 奥克语" lang="oc" hreflang="oc" data-title="Infinit" data-language-autonym="Occitan" data-language-local-name="奥克语" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%A8%E0%A9%B0%E0%A8%A4" title="ਅਨੰਤ – 旁遮普语" lang="pa" hreflang="pa" data-title="ਅਨੰਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="旁遮普语" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Niesko%C5%84czono%C5%9B%C4%87" title="Nieskończoność – 波兰语" lang="pl" hreflang="pl" data-title="Nieskończoność" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Infin%C3%AC" title="Infinì – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Infinì" data-language-autonym="Piemontèis" data-language-local-name="皮埃蒙特文" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%86%D8%A7%D9%86%D8%AA%DB%8C" title="انانتی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انانتی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Infinito" title="Infinito – 葡萄牙语" lang="pt" hreflang="pt" data-title="Infinito" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Infinit" title="Infinit – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Infinit" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Бесконечность – 俄语" lang="ru" hreflang="ru" data-title="Бесконечность" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Бесконечность – 盧森尼亞文" lang="rue" hreflang="rue" data-title="Бесконечность" data-language-autonym="Русиньскый" data-language-local-name="盧森尼亞文" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Nfinitu_(matim%C3%A0tica)" title="Nfinitu (matimàtica) – 西西里语" lang="scn" hreflang="scn" data-title="Nfinitu (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="西西里语" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Infinity" title="Infinity – 苏格兰语" lang="sco" hreflang="sco" data-title="Infinity" data-language-autonym="Scots" data-language-local-name="苏格兰语" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Beskona%C4%8Dnost_(matematika)" title="Beskonačnost (matematika) – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Beskonačnost (matematika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%85%E0%B6%B1%E0%B6%B1%E0%B7%8A%E0%B6%AD%E0%B6%BA" title="අනන්තය – 僧伽罗语" lang="si" hreflang="si" data-title="අනන්තය" data-language-autonym="සිංහල" data-language-local-name="僧伽罗语" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Infinity" title="Infinity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Infinity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Nekone%C4%8Dno" title="Nekonečno – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Nekonečno" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Neskon%C4%8Dnost" title="Neskončnost – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Neskončnost" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Kusingaperi" title="Kusingaperi – 绍纳语" lang="sn" hreflang="sn" data-title="Kusingaperi" data-language-autonym="ChiShona" data-language-local-name="绍纳语" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Pafund%C3%ABsia" title="Pafundësia – 阿尔巴尼亚语" lang="sq" hreflang="sq" data-title="Pafundësia" data-language-autonym="Shqip" data-language-local-name="阿尔巴尼亚语" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B0%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Бесконачност – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Бесконачност" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/O%C3%A4ndlighet" title="Oändlighet – 瑞典语" lang="sv" hreflang="sv" data-title="Oändlighet" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AE%BF" title="முடிவிலி – 泰米尔语" lang="ta" hreflang="ta" data-title="முடிவிலி" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%91%D0%B5%D0%B8%D0%BD%D1%82%D0%B8%D2%B3%D0%BE%D3%A3" title="Беинтиҳоӣ – 塔吉克语" lang="tg" hreflang="tg" data-title="Беинтиҳоӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="塔吉克语" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%99%E0%B8%B1%E0%B8%99%E0%B8%95%E0%B9%8C" title="อนันต์ – 泰语" lang="th" hreflang="th" data-title="อนันต์" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kawalang-hanggan" title="Kawalang-hanggan – 他加禄语" lang="tl" hreflang="tl" data-title="Kawalang-hanggan" data-language-autonym="Tagalog" data-language-local-name="他加禄语" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sonsuz" title="Sonsuz – 土耳其语" lang="tr" hreflang="tr" data-title="Sonsuz" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A7%D0%B8%D0%BA%D1%81%D0%B5%D0%B7%D0%BB%D0%B5%D0%BA" title="Чиксезлек – 鞑靼语" lang="tt" hreflang="tt" data-title="Чиксезлек" data-language-autonym="Татарча / tatarça" data-language-local-name="鞑靼语" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9D%D0%B5%D1%81%D0%BA%D1%96%D0%BD%D1%87%D0%B5%D0%BD%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Нескінченність – 乌克兰语" lang="uk" hreflang="uk" data-title="Нескінченність" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%AA%D9%86%D8%A7%DB%81%DB%8C_%D8%A7%D9%88%D8%B1_%D9%84%D8%A7%D9%85%D8%AA%D9%86%D8%A7%DB%81%DB%8C" title="متناہی اور لامتناہی – 乌尔都语" lang="ur" hreflang="ur" data-title="متناہی اور لامتناہی" data-language-autonym="اردو" data-language-local-name="乌尔都语" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Cheksizlik" title="Cheksizlik – 乌兹别克语" lang="uz" hreflang="uz" data-title="Cheksizlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="乌兹别克语" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Lopm%C3%A4tomuz" title="Lopmätomuz – 维普森语" lang="vep" hreflang="vep" data-title="Lopmätomuz" data-language-autonym="Vepsän kel’" data-language-local-name="维普森语" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%C3%B4_t%E1%BA%ADn" title="Vô tận – 越南语" lang="vi" hreflang="vi" data-title="Vô tận" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Infinidad" title="Infinidad – 瓦瑞语" lang="war" hreflang="war" data-title="Infinidad" data-language-autonym="Winaray" data-language-local-name="瓦瑞语" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%97%A0%E7%A9%B7" title="无穷 – 吴语" lang="wuu" hreflang="wuu" data-title="无穷" data-language-autonym="吴语" data-language-local-name="吴语" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%95%D7%9E%D7%A2%D7%A0%D7%93%D7%9C%D7%A2%D7%9B%D7%A7%D7%99%D7%99%D7%98" title="אומענדלעכקייט – 意第绪语" lang="yi" hreflang="yi" data-title="אומענדלעכקייט" data-language-autonym="ייִדיש" data-language-local-name="意第绪语" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%84%A1%E9%99%90" title="無限 – 文言文" lang="lzh" hreflang="lzh" data-title="無限" data-language-autonym="文言" data-language-local-name="文言文" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/B%C3%BB-h%C4%81n" title="Bû-hān – 闽南语" lang="nan" hreflang="nan" data-title="Bû-hān" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="闽南语" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%84%A1%E7%AA%AE%E7%9B%A1" title="無窮盡 – 粤语" lang="yue" hreflang="yue" data-title="無窮盡" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q205#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="命名空间"> <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/%E6%97%A0%E7%A9%B7" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E6%97%A0%E7%A9%B7" rel="discussion" title="关于此页面的讨论[t]" accesskey="t"><span>讨论</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " > <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="更改语言变体" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">不转换</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-zh mw-list-item"><a href="/zh/%E6%97%A0%E7%A9%B7" lang="zh" hreflang="zh"><span>不转换</span></a></li><li id="ca-varlang-1" class="ca-variants-zh-Hans mw-list-item"><a href="/zh-hans/%E6%97%A0%E7%A9%B7" lang="zh-Hans" hreflang="zh-Hans"><span>简体</span></a></li><li id="ca-varlang-2" class="ca-variants-zh-Hant mw-list-item"><a href="/zh-hant/%E6%97%A0%E7%A9%B7" lang="zh-Hant" hreflang="zh-Hant"><span>繁體</span></a></li><li id="ca-varlang-3" class="ca-variants-zh-Hans-CN mw-list-item"><a href="/zh-cn/%E6%97%A0%E7%A9%B7" lang="zh-Hans-CN" hreflang="zh-Hans-CN"><span>大陆简体</span></a></li><li id="ca-varlang-4" class="ca-variants-zh-Hant-HK mw-list-item"><a href="/zh-hk/%E6%97%A0%E7%A9%B7" lang="zh-Hant-HK" hreflang="zh-Hant-HK"><span>香港繁體</span></a></li><li id="ca-varlang-5" class="ca-variants-zh-Hant-MO mw-list-item"><a href="/zh-mo/%E6%97%A0%E7%A9%B7" lang="zh-Hant-MO" hreflang="zh-Hant-MO"><span>澳門繁體</span></a></li><li id="ca-varlang-6" class="ca-variants-zh-Hans-MY mw-list-item"><a href="/zh-my/%E6%97%A0%E7%A9%B7" lang="zh-Hans-MY" hreflang="zh-Hans-MY"><span>大马简体</span></a></li><li id="ca-varlang-7" class="ca-variants-zh-Hans-SG mw-list-item"><a href="/zh-sg/%E6%97%A0%E7%A9%B7" lang="zh-Hans-SG" hreflang="zh-Hans-SG"><span>新加坡简体</span></a></li><li id="ca-varlang-8" class="ca-variants-zh-Hant-TW mw-list-item"><a href="/zh-tw/%E6%97%A0%E7%A9%B7" lang="zh-Hant-TW" hreflang="zh-Hant-TW"><span>臺灣正體</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="查看"> <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/%E6%97%A0%E7%A9%B7"><span>阅读</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=history" title="本页面的早前版本。[h]" accesskey="h"><span>查看历史</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <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="工具" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">工具</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">工具</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">隐藏</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="更多选项" > <div class="vector-menu-heading"> 操作 </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/%E6%97%A0%E7%A9%B7"><span>阅读</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=history"><span>查看历史</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 常规 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%85%A5%E9%A1%B5%E9%9D%A2/%E6%97%A0%E7%A9%B7" title="列出所有与本页相链的页面[j]" accesskey="j"><span>链入页面</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%87%BA%E6%9B%B4%E6%94%B9/%E6%97%A0%E7%A9%B7" rel="nofollow" title="页面链出所有页面的更改[k]" accesskey="k"><span>相关更改</span></a></li><li id="t-upload" class="mw-list-item"><a href="//zh.wikipedia.org/wiki/Project:上传" title="上传图像或多媒体文件[u]" accesskey="u"><span>上传文件</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&oldid=86134539" title="此页面该修订版本的固定链接"><span>固定链接</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=info" title="关于此页面的更多信息"><span>页面信息</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:%E5%BC%95%E7%94%A8%E6%AD%A4%E9%A1%B5%E9%9D%A2&page=%E6%97%A0%E7%A9%B7&id=86134539&wpFormIdentifier=titleform" title="有关如何引用此页面的信息"><span>引用此页</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:URL%E7%BC%A9%E7%9F%AD%E7%A8%8B%E5%BA%8F&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E6%2597%25A0%25E7%25A9%25B7"><span>获取短链接</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E6%2597%25A0%25E7%25A9%25B7"><span>下载二维码</span></a></li> </ul> </div> </div> <div id="p-electronpdfservice-sidebar-portlet-heading" class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 打印/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E6%97%A0%E7%A9%B7&action=show-download-screen"><span>下载为PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p"><span>打印页面</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 在其他项目中 </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:Infinity" hreflang="en"><span>维基共享资源</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q205" title="链接到连接的数据仓库项目[g]" accesskey="g"><span>维基数据项目</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <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">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-noteTA-307af9e9" class="mw-indicator"><div class="mw-parser-output"><span class="skin-invert" typeof="mw:File"><span title="本页使用了标题或全文手工转换"><img alt="本页使用了标题或全文手工转换" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></span></span></div></div> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">（重定向自<a href="/w/index.php?title=%E6%97%A0%E7%A9%B7%E5%A4%A7&redirect=no" class="mw-redirect" title="无穷大">无穷大</a>）</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><div id="noteTA-307af9e9" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Math"></div></div></div> <style data-mw-deduplicate="TemplateStyles:r85100532">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable"><span class="noviewer hatnote-notice-img" typeof="mw:File"><a href="/wiki/Wikipedia:%E6%B6%88%E6%AD%A7%E4%B9%89" title="Wikipedia:消歧义"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/25px-Disambig_gray.svg.png" decoding="async" width="25" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/38px-Disambig_gray.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/50px-Disambig_gray.svg.png 2x" data-file-width="220" data-file-height="168" /></a></span>「<b>无限</b>」重定向至此。关于其他用法，请见「<b><a href="/wiki/%E6%97%A0%E9%99%90_(%E6%B6%88%E6%AD%A7%E4%B9%89)" class="mw-disambig" title="无限 (消歧义)">无限 (消歧义)</a></b>」。</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable"><span class="noviewer hatnote-notice-img" typeof="mw:File"><a href="/wiki/Wikipedia:%E6%B6%88%E6%AD%A7%E4%B9%89" title="Wikipedia:消歧义"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/25px-Disambig_gray.svg.png" decoding="async" width="25" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/38px-Disambig_gray.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/50px-Disambig_gray.svg.png 2x" data-file-width="220" data-file-height="168" /></a></span>「<b>无数</b>」重定向至此。关于其他用法，请见「<b><a href="/wiki/%E6%97%A0%E6%95%B0_(%E4%B8%93%E8%BE%91)" title="无数 (专辑)">无数 (专辑)</a></b>」。</div> <table class="floatright toc" style="width:260px; margin: 0 0 1em 1em"> <tbody><tr style="background:#ccccff" align="center"> <td style="border-bottom: 2px solid #303060"><b>各种各样的<a href="/wiki/%E6%95%B0" title="数">数</a></b> </td></tr> <tr style="background:#ccccff" align="center"> <td><b>基本</b> </td></tr> <tr align="center"> <td> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {N} \subseteq \mathbb {Z} \subseteq \mathbb {Q} \subseteq \mathbb {R} \subseteq \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mo>⊆</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>⊆</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mo>⊆</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>⊆</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} \subseteq \mathbb {Z} \subseteq \mathbb {Q} \subseteq \mathbb {R} \subseteq \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ba5a9ecbc18a9d9c1b0af89662b4452b7e9c0a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.787ex; height:2.509ex;" alt="{\displaystyle \mathbb {N} \subseteq \mathbb {Z} \subseteq \mathbb {Q} \subseteq \mathbb {R} \subseteq \mathbb {C} }"></span> <span class="skin-invert" typeof="mw:File"><a href="/wiki/File:NumberSetinC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/NumberSetinC.svg/250px-NumberSetinC.svg.png" decoding="async" width="250" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/NumberSetinC.svg/375px-NumberSetinC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/NumberSetinC.svg/500px-NumberSetinC.svg.png 2x" data-file-width="600" data-file-height="470" /></a></span> <style data-mw-deduplicate="TemplateStyles:r82553231">@media all and (max-width:720px){.mw-parser-output table.multicol>tr>td,.mw-parser-output table.multicol>tbody>tr>td{display:block!important;width:100%!important;padding:0!important}}.mw-parser-output table.multicol{border:0;border-collapse:collapse;background-color:transparent;color:inherit;padding:0}.mw-parser-output table.multicol>tr>td,.mw-parser-output table.multicol>tbody>tr>td{vertical-align:top!important}</style> </p> <div>   <table class="multicol" role="presentation" style="width:100%;"><tbody><tr> <td style="width: 50%;text-align: left;vertical-align: top;"> <p><a href="/wiki/%E6%AD%A3%E6%95%B8" title="正數">正數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{+}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97dc5e850d079061c24290bac160c8d3b62ee139" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.189ex; height:2.509ex;" alt="{\displaystyle \mathbb {R} ^{+}}"></span><br /> <a href="/wiki/%E8%87%AA%E7%84%B6%E6%95%B0" title="自然数">自然数</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf9a96b565ea202d0f4322e9195613fb26a9bed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {N} }"></span><br /> <a href="/wiki/%E8%87%AA%E7%84%B6%E6%95%B0" title="自然数">正整數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} ^{+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} ^{+}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/628778fcf14bd3629e9b9ebacffa172b0ad6ce41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.061ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} ^{+}}"></span><br /> <a href="/wiki/%E5%B0%8F%E6%95%B0" title="小数">小数</a><br /> <a href="/wiki/%E6%9C%89%E9%99%90%E5%B0%8F%E6%95%B0" title="有限小数">有限小数</a><br /> <a href="/wiki/%E6%97%A0%E9%99%90%E5%B0%8F%E6%95%B0" title="无限小数">无限小数</a><br /> <a href="/wiki/%E5%BE%AA%E7%8E%AF%E5%B0%8F%E6%95%B0" title="循环小数">循环小数</a><br /> <a href="/wiki/%E6%9C%89%E7%90%86%E6%95%B0" title="有理数">有理数</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="{\displaystyle \mathbb {Q} }"></span><br /> <a href="/wiki/%E4%BB%A3%E6%95%B8%E6%95%B8" title="代數數">代數數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fb423c16a5f403edbaf66438b75e7a36e725af6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {A} }"></span><br /> <a href="/wiki/%E5%AE%9E%E6%95%B0" title="实数">实数</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {R} }"></span><br /> <a href="/wiki/%E5%A4%8D%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="复数 (数学)">複數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {C} }"></span><br /> <a href="/wiki/%E9%AB%98%E6%96%AF%E6%95%B4%E6%95%B8" title="高斯整數">高斯整數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} [i]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo stretchy="false">[</mo> <mi>i</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} [i]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ffa94e9e2e6d9e5e5373d5fafb954b902743fde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.646ex; height:2.843ex;" alt="{\displaystyle \mathbb {Z} [i]}"></span><br />   </p> </td> <td style="width: 50%;text-align: left;vertical-align: top;"> <p><a href="/wiki/%E8%B4%9F%E6%95%B0" title="负数">负数</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{-}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{-}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/158001a03e958f49f5885033776a420fc47b7267" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.189ex; height:2.509ex;" alt="{\displaystyle \mathbb {R} ^{-}}"></span><br /> <a href="/wiki/%E6%95%B4%E6%95%B0" title="整数">整数</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle \mathbb {Z} }"></span><br /> <a href="/wiki/%E8%B2%A0%E6%95%B4%E6%95%B8" title="負整數">负整數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} ^{-}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} ^{-}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d265f6ad41c1623a6477b2cb4336208c7b6c1d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.061ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} ^{-}}"></span><br /> <a href="/wiki/%E5%88%86%E6%95%B8" title="分數">分數</a><br /> <a href="/wiki/%E5%96%AE%E4%BD%8D%E5%88%86%E6%95%B8" title="單位分數">單位分數</a><br /> <a href="/wiki/%E4%BA%8C%E8%BF%9B%E5%88%86%E6%95%B0" title="二进分数">二进分数</a><br /> <a href="/wiki/%E8%A6%8F%E7%9F%A9%E6%95%B8" title="規矩數">規矩數</a><br /> <a href="/wiki/%E7%84%A1%E7%90%86%E6%95%B8" title="無理數">無理數</a><br /> <a href="/wiki/%E8%B6%85%E8%B6%8A%E6%95%B8" title="超越數">超越數</a><br /> <a href="/wiki/%E8%99%9A%E6%95%B0" title="虚数">虚数</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8205f06e0d279689ed04a1ac04a3d9c249c637df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.905ex; height:2.176ex;" alt="{\displaystyle \mathbb {I} }"></span><br /> <a href="/wiki/%E4%BA%8C%E6%AC%A1%E7%84%A1%E7%90%86%E6%95%B8" title="二次無理數">二次無理數</a><br /> <a href="/wiki/%E8%89%BE%E6%A3%AE%E6%96%AF%E5%9D%A6%E6%95%B4%E6%95%B0" title="艾森斯坦整数">艾森斯坦整数</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} [\omega ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo stretchy="false">[</mo> <mi>ω</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} [\omega ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae955a9a0d0f342fc73aaafe28af604d23267f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.29ex; height:2.843ex;" alt="{\displaystyle \mathbb {Z} [\omega ]}"></span><br />   </p> </td></tr></tbody></table></div> </td></tr> <tr style="background:#ccccff" align="center"> <td><b>延伸</b> </td></tr> <tr align="center"> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r82553231"> <div>   <table class="multicol" role="presentation" style="width:100%;"><tbody><tr> <td style="width: 50%;text-align: left;vertical-align: top;"> <p><a href="/wiki/%E4%BA%8C%E5%85%83%E6%95%B0" title="二元数">二元数</a><br /> <a href="/wiki/%E5%9B%9B%E5%85%83%E6%95%B8" title="四元數">四元數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {H} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">H</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {H} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e050965453c42bcc6bd544546703c836bdafeac9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \mathbb {H} }"></span><br /> <a href="/wiki/%E5%85%AB%E5%85%83%E6%95%B0" title="八元数">八元数</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {O} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">O</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {O} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1ed2664a4fe515e6fbed25a7193ce663b82920c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \mathbb {O} }"></span><br /> <a href="/wiki/%E5%8D%81%E5%85%AD%E5%85%83%E6%95%B8" title="十六元數">十六元數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {S} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f9d5874c5d7f68eba1cec9da9ccbe53903303bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.293ex; height:2.176ex;" alt="{\displaystyle \mathbb {S} }"></span><br /> <a href="/wiki/%E8%B6%85%E5%AE%9E%E6%95%B0_(%E9%9D%9E%E6%A0%87%E5%87%86%E5%88%86%E6%9E%90)" title="超实数 (非标准分析)">超實數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{*}\mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{*}\mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4df367c74a9138be68469102a92d2fa8cbc15f6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.732ex; height:2.343ex;" alt="{\displaystyle ^{*}\mathbb {R} }"></span><br /> <a href="/w/index.php?title=%E5%A4%A7%E5%AF%A6%E6%95%B8&action=edit&redlink=1" class="new" title="大實數（页面不存在）">大實數</a><br /> <a href="/w/index.php?title=%E4%B8%8A%E8%B6%85%E5%AF%A6%E6%95%B8&action=edit&redlink=1" class="new" title="上超實數（页面不存在）">上超實數</a><br />   </p> </td> <td style="width: 50%;text-align: left;vertical-align: top;"> <p><a href="/wiki/%E9%9B%99%E6%9B%B2%E8%A4%87%E6%95%B8" title="雙曲複數">雙曲複數</a><br /> <a href="/wiki/%E9%9B%99%E8%A4%87%E6%95%B8" title="雙複數">雙複數</a><br /> <a href="/wiki/%E8%A4%87%E5%9B%9B%E5%85%83%E6%95%B8" title="複四元數">複四元數</a><br /> <span class="ilh-all" data-orig-title="共四元數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Dual quaternion"><span class="ilh-page"><a href="/w/index.php?title=%E5%85%B1%E5%9B%9B%E5%85%83%E6%95%B8&action=edit&redlink=1" class="new" title="共四元數（页面不存在）">共四元數</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Dual_quaternion" class="extiw" title="en:Dual quaternion"><span lang="en" dir="auto">Dual quaternion</span></a></span><span class="ilh-paren">）</span></span></span><br /> <a href="/wiki/%E8%B6%85%E5%A4%8D%E6%95%B0" title="超复数">超复数</a><br /> <a href="/w/index.php?title=%E8%B6%85%E6%95%B8&action=edit&redlink=1" class="new" title="超數（页面不存在）">超數</a><br /> <a href="/wiki/%E8%B6%85%E7%8F%BE%E5%AF%A6%E6%95%B8" title="超現實數">超現實數</a><br />   </p> </td></tr></tbody></table></div> </td></tr> <tr style="background:#ccccff" align="center"> <td><b>其他</b> </td></tr> <tr align="center"> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r82553231"> <div>   <table class="multicol" role="presentation" style="width:100%;"><tbody><tr> <td style="width: 50%;text-align: left;vertical-align: top;"> <p><a href="/wiki/%E8%B4%A8%E6%95%B0" title="质数">質數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {P} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">P</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {P} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1053af9e662ceaf56c4455f90e0f67273422eded" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.42ex; height:2.176ex;" alt="{\displaystyle \mathbb {P} }"></span><br /> <a href="/wiki/%E5%8F%AF%E8%A8%88%E7%AE%97%E6%95%B8" title="可計算數">可計算數</a><br /> <a href="/wiki/%E5%9F%BA%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="基数 (数学)">基數</a><br /> <a href="/wiki/%E9%98%BF%E5%88%97%E5%A4%AB%E6%95%B8" title="阿列夫數">阿列夫數</a><br /> <a href="/wiki/%E5%90%8C%E9%A4%98" title="同餘">同餘</a><br /> <a href="/wiki/%E6%95%B4%E6%95%B8%E6%95%B8%E5%88%97" title="整數數列">整數數列</a><br /> <a href="/w/index.php?title=%E5%85%AC%E7%A8%B1%E5%80%BC&action=edit&redlink=1" class="new" title="公稱值（页面不存在）">公稱值</a><br />   </p> </td> <td style="width: 50%;text-align: left;vertical-align: top;"> <p><a href="/wiki/%E8%A6%8F%E7%9F%A9%E6%95%B8" title="規矩數">規矩數</a><br /> <a href="/wiki/%E5%8F%AF%E5%AE%9A%E4%B9%89%E6%95%B0" title="可定义数">可定义数</a><br /> <a href="/wiki/%E5%BA%8F%E6%95%B0" title="序数">序数</a><br /> <a href="/wiki/%E8%B6%85%E9%99%90%E6%95%B0" title="超限数">超限数</a><br /> <a href="/wiki/P%E9%80%B2%E6%95%B8" title="P進數"><style data-mw-deduplicate="TemplateStyles:r58896141">'"`UNIQ--templatestyles-0000001C-QINU`"'</style><span class="serif"><span class="texhtml"><i>p</i></span></span>進數</a><br /> <a href="/wiki/%E6%95%B0%E5%AD%A6%E5%B8%B8%E6%95%B0" title="数学常数">数学常数</a><br />   </p> </td></tr></tbody></table></div> <p><a href="/wiki/%E5%9C%93%E5%91%A8%E7%8E%87" title="圓周率">圓周率</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi =3.14159265}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo>=</mo> <mn>3.14159265</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi =3.14159265}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d789e69af1e86cd0404c764423ff0c104108f1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.539ex; height:2.176ex;" alt="{\displaystyle \pi =3.14159265}"></span>…<br /> <a href="/wiki/E_(%E6%95%B0%E5%AD%A6%E5%B8%B8%E6%95%B0)" title="E (数学常数)">自然對數的底</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e=2.718281828}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mn>2.718281828</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e=2.718281828}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1855c2b5b2d2768a0b909ffbc16cf9a18bb11845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.453ex; height:2.176ex;" alt="{\displaystyle e=2.718281828}"></span>…<br /> <a href="/wiki/%E8%99%9B%E6%95%B8%E5%96%AE%E4%BD%8D" title="虛數單位">虛數單位</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i={\sqrt {-{1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i={\sqrt {-{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b13bc2b4f7e103e92342633692e46d585913f342" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.807ex; height:3.009ex;" alt="{\displaystyle i={\sqrt {-{1}}}}"></span><br /> <a class="mw-selflink selflink">無限大</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> </p> </td></tr> <tr> <td align="right"><style data-mw-deduplicate="TemplateStyles:r84265675">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:" :"}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist-pipe dd::after,.mw-parser-output .hlist-pipe li::after{content:" | ";font-weight:normal}.mw-parser-output .hlist-hyphen dd::after,.mw-parser-output .hlist-hyphen li::after{content:" - ";font-weight:normal}.mw-parser-output .hlist-comma dd::after,.mw-parser-output .hlist-comma li::after{content:"、";font-weight:normal}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:"（"counter(listitem)"\a0 "}.mw-parser-output ul.cslist,.mw-parser-output ul.sslist{margin:0;padding:0;display:inline-block;list-style:none}.mw-parser-output .cslist li,.mw-parser-output .sslist li{margin:0;display:inline-block}.mw-parser-output .cslist li::after{content:"，"}.mw-parser-output .sslist li::after{content:"；"}.mw-parser-output .cslist li:last-child::after,.mw-parser-output .sslist li:last-child::after{content:none}</style><style data-mw-deduplicate="TemplateStyles:r84244141">.mw-parser-output .navbar{display:inline;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:110%;margin:0 8em}.mw-parser-output .navbar-ct-mini{font-size:110%;margin:0 5em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E6%95%B8" title="Template:數"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E6%95%B8" title="Template talk:數"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E6%95%B8" title="Special:编辑页面/Template:數"><abbr title="编辑该模板">编</abbr></a></li></ul></div> </td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Infinity_symbol.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Infinity_symbol.svg/200px-Infinity_symbol.svg.png" decoding="async" width="200" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Infinity_symbol.svg/300px-Infinity_symbol.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Infinity_symbol.svg/400px-Infinity_symbol.svg.png 2x" data-file-width="420" data-file-height="475" /></a><figcaption>不同字體下的∞符號</figcaption></figure> <p><b>無窮</b>（英語：<span lang="en">infinity</span>，又稱<b>無限大</b>），來自於<a href="/wiki/%E6%8B%89%E4%B8%81%E6%96%87" class="mw-redirect" title="拉丁文">拉丁文</a>的「infinitas」，即「沒有邊界」的意思。其<a href="/wiki/%E6%95%B8%E5%AD%B8" class="mw-redirect" title="數學">數學</a><a href="/wiki/%E7%AC%A6%E8%99%9F" class="mw-redirect" title="符號">符號</a>為∞。它在<a href="/wiki/%E7%A7%91%E5%AD%B8" class="mw-redirect" title="科學">科學</a>、<a href="/wiki/%E7%A5%9E%E5%AD%B8" title="神學">神學</a>、<a href="/wiki/%E5%93%B2%E5%AD%B8" class="mw-redirect" title="哲學">哲學</a>、<a href="/wiki/%E6%95%B8%E5%AD%B8" class="mw-redirect" title="數學">數學</a>和日常生活中有著不同的概念。通常使用這個詞的時候並不涉及它的更加技術層面的定義。 </p><p>在神學方面，根據書面記載<b>無窮</b>這個符號最早被用於某些秘密宗教，通常代表人類中的神性，而書寫此符號時兩圓的不對等代表人神間的差距，例如神學家<a href="/wiki/%E9%82%93%E6%96%AF%C2%B7%E5%8F%B8%E5%90%84%E8%84%B1" title="邓斯·司各脱">邓斯·司各脱</a>（Duns Scotus）的著作中，上帝的無限能量是運用在無約束上，而不是運用在無限量上。在哲學方面，無窮可以歸因於空間和時間。在神學和哲學兩方面，無窮又作為無限，很多文章都探討過無限、絕對、上帝和<a href="/wiki/%E8%8A%9D%E8%AB%BE%E6%82%96%E8%AB%96" class="mw-redirect" title="芝諾悖論">芝諾悖論</a>等的問題。 </p><p>在數學方面，無窮與下述的主題或概念相關：數學的<a href="/wiki/%E6%A5%B5%E9%99%90_(%E6%95%B8%E5%AD%B8)" class="mw-redirect" title="極限 (數學)">極限</a>、<a href="/wiki/%E9%98%BF%E5%88%97%E5%A4%AB%E6%95%B8" title="阿列夫數">阿列夫數</a>、<a href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" class="mw-redirect" title="集合論">集合論</a>中的<a href="/wiki/%E9%A1%9E_(%E6%95%B8%E5%AD%B8)" class="mw-redirect" title="類 (數學)">類</a>、<span class="ilh-all" data-orig-title="戴德金無限集合" data-lang-code="en" data-lang-name="英语" data-foreign-title="Dedekind-infinite set"><span class="ilh-page"><a href="/w/index.php?title=%E6%88%B4%E5%BE%B7%E9%87%91%E7%84%A1%E9%99%90%E9%9B%86%E5%90%88&action=edit&redlink=1" class="new" title="戴德金無限集合（页面不存在）">戴德金無限集合</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Dedekind-infinite_set" class="extiw" title="en:Dedekind-infinite set"><span lang="en" dir="auto">Dedekind-infinite set</span></a></span><span class="ilh-paren">）</span></span></span>、<a href="/wiki/%E7%BE%85%E7%B4%A0%E6%82%96%E8%AB%96" class="mw-redirect" title="羅素悖論">羅素悖論</a>、<a href="/wiki/%E8%B6%85%E5%AE%9E%E6%95%B0_(%E9%9D%9E%E6%A0%87%E5%87%86%E5%88%86%E6%9E%90)" title="超实数 (非标准分析)">超實數</a>、<a href="/wiki/%E5%B0%84%E5%BD%B1%E5%B9%BE%E4%BD%95" class="mw-redirect" title="射影幾何">射影幾何</a>、<a href="/wiki/%E6%89%A9%E5%B1%95%E7%9A%84%E5%AE%9E%E6%95%B0%E8%BD%B4" class="mw-redirect" title="扩展的实数轴">擴展的實數軸</a>以及<a href="/wiki/%E7%B5%95%E5%B0%8D%E7%84%A1%E9%99%90" class="mw-redirect" title="絕對無限">絕對無限</a>。在一些主題或概念中，無窮被認為是一個超越邊界而增加的概念，而不是一個數。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="歷史"><span id=".E6.AD.B7.E5.8F.B2"></span>歷史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=1" title="编辑章节：歷史"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="早期無限的觀點"><span id=".E6.97.A9.E6.9C.9F.E7.84.A1.E9.99.90.E7.9A.84.E8.A7.80.E9.BB.9E"></span>早期無限的觀點</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=2" title="编辑章节：早期無限的觀點"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>最早關於無限的記載出現在<a href="/wiki/%E5%8D%B0%E5%BA%A6" title="印度">印度</a>的<a href="/wiki/%E5%A4%9C%E6%9F%94%E5%90%A0%E9%99%80" title="夜柔吠陀">夜柔吠陀</a>（公元前1200－900）。書中說：「如果你從無限中移走或添加一部分，剩下的還是無限。」 </p><p>印度<a href="/wiki/%E8%80%86%E9%82%A3%E6%95%99" title="耆那教">耆那教</a>的經書《Surya Prajnapti》（c. 400 BC）把數分作三類：「可計的」、「不可計的」及「無限」。每一類再細分成三種階： </p> <ul><li>可計的：小的、中的與大的。</li> <li>不可計的：接近不可計的、真正不可計的、沒有方法去計的，以及無限也包括在內。</li> <li>無限：接近無限、真正無限與無窮無盡。</li></ul> <p>現代科學家解析古代羊皮卷中的阿基米德手稿（<span class="ilh-all" data-orig-title="Archimedes Palimpsest" data-lang-code="en" data-lang-name="英语" data-foreign-title="Archimedes Palimpsest"><span class="ilh-page"><a href="/w/index.php?title=Archimedes_Palimpsest&action=edit&redlink=1" class="new" title="Archimedes Palimpsest（页面不存在）">Archimedes Palimpsest</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Archimedes_Palimpsest" class="extiw" title="en:Archimedes Palimpsest"><span lang="en" dir="auto">Archimedes Palimpsest</span></a></span><span class="ilh-paren">）</span></span></span>），在殘卷《方法》命題14中，發現阿基米德開始計算<a href="/wiki/%E6%97%A0%E7%A9%B7%E5%A4%A7" class="mw-redirect" title="无穷大">無窮大</a>的數目。他採取近似於19世紀<a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" class="mw-redirect" title="微積分">微積分</a>與<a href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" class="mw-redirect" title="集合論">集合論</a>的手法，計算了兩組無窮大的<a href="/wiki/%E9%9B%86%E5%90%88_(%E6%95%B0%E5%AD%A6)" title="集合 (数学)">集合</a>，以求和的方法，證明它們之間的數目是相等的。 </p><p>這是在人類記載上第一次出現無限也可以分類這一個念頭。 </p> <div class="mw-heading mw-heading3"><h3 id="文藝復興時代至近代"><span id=".E6.96.87.E8.97.9D.E5.BE.A9.E8.88.88.E6.99.82.E4.BB.A3.E8.87.B3.E8.BF.91.E4.BB.A3"></span>文藝復興時代至近代</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=3" title="编辑章节：文藝復興時代至近代"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>伽利略最先發現一個集合跟它自己的真子集可以有相同的大小。 </p><p>他用上一一對應的概念說明自然數集{1, 2, 3, 4, ...}跟子集平方數集{1, 4, 9, 16, ...}一樣多。就是1→1、2→4、3→9、4→16、..... </p><p>一一對應正是用於研究無限必要的手法。 </p> <div class="mw-heading mw-heading2"><h2 id="數學中的無窮"><span id=".E6.95.B8.E5.AD.B8.E4.B8.AD.E7.9A.84.E7.84.A1.E7.AA.AE"></span>數學中的無窮</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=4" title="编辑章节：數學中的無窮"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="無限大的符號"><span id=".E7.84.A1.E9.99.90.E5.A4.A7.E7.9A.84.E7.AC.A6.E8.99.9F"></span>無限大的符號</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=5" title="编辑章节：無限大的符號"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>無限大的符號是<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span>，其<a href="/wiki/Unicode" title="Unicode">Unicode</a>為<span class="nowrap"><style data-mw-deduplicate="TemplateStyles:r79829556">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">U+221E</span></span> <span style="font-size:200%;line-height:1em">∞</span> <style data-mw-deduplicate="TemplateStyles:r71146900">.mw-parser-output .smallcaps-all{font-variant:small-caps;text-transform:lowercase}.mw-parser-output .smallcaps-all>span{font-variant:normal;text-transform:none}</style><span class="smallcaps-all">INFINITY</span>，在<a href="/wiki/LaTeX" title="LaTeX">LaTeX</a>中表示為<code>\infty</code>。 </p><p>無限大的符號是1655年由<a href="/wiki/%E7%B4%84%E7%BF%B0%C2%B7%E6%B2%83%E5%88%A9%E6%96%AF" title="約翰·沃利斯">約翰·沃利斯</a>開始使用<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>，在開始使用後，也用在數學以外的領域，例如現代神祕主義<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>及符號學<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="微積分及實分析中的無窮"><span id=".E5.BE.AE.E7.A9.8D.E5.88.86.E5.8F.8A.E5.AF.A6.E5.88.86.E6.9E.90.E4.B8.AD.E7.9A.84.E7.84.A1.E7.AA.AE"></span>微積分及實分析中的無窮</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=6" title="编辑章节：微積分及實分析中的無窮"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E8%8E%B1%E5%B8%83%E5%B0%BC%E8%8C%A8" class="mw-redirect" title="莱布尼茨">莱布尼茨</a>是提出許多有關其在數學中應用的猜測。對莱布尼茨而言，无穷大和<a href="/wiki/%E7%84%A1%E7%AA%AE%E5%B0%8F%E9%87%8F" title="無窮小量">無窮小量</a>都是理想的實體，和一般數值的本質不同，不過有類似的性質<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>。 </p><p>在<a href="/wiki/%E5%AF%A6%E5%88%86%E6%9E%90" class="mw-redirect" title="實分析">實分析</a>中，符號<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span>稱為「無窮大」，代表無界<a href="/wiki/%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90" class="mw-redirect" title="函数极限">極限</a>。<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\to +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">→</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\to +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac2c4d9c1dd87b1f5715377dc1847793939a93a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.076ex; height:2.176ex;" alt="{\displaystyle x\to +\infty }"></span>表示<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\quad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e41a831f1ca13946b4e2277ea1b9bbc1aa08709" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.652ex; height:1.676ex;" alt="{\displaystyle x\quad }"></span>超出任意給定值，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\to -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">→</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\to -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a02931d12f93c144745ec549edf61e85fba2c3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.076ex; height:2.176ex;" alt="{\displaystyle x\to -\infty }"></span>表示<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\quad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e41a831f1ca13946b4e2277ea1b9bbc1aa08709" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.652ex; height:1.676ex;" alt="{\displaystyle x\quad }"></span>最終小於任意給定值。 </p><p>一函數積分的結果可能會是無限大，若對於所有的<i>t</i>，<i>f</i>(<i>t</i>) ≥ 0，則<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{a}^{b}\,f(t)\ dt\ =\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mspace width="thinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>d</mi> <mi>t</mi> <mtext> </mtext> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{a}^{b}\,f(t)\ dt\ =\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09ccbfcbaacc342f897b21041655bbe13566d87d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.742ex; height:6.343ex;" alt="{\displaystyle \int _{a}^{b}\,f(t)\ dt\ =\infty }"></span> 意思是<i>f</i>(<i>t</i>) 在<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>到<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>的範圍內，其面積是無限大。</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{-\infty }^{\infty }\,f(t)\ dt\ =\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mspace width="thinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>d</mi> <mi>t</mi> <mtext> </mtext> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{-\infty }^{\infty }\,f(t)\ dt\ =\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35997478613fc24e1c6a72ef5ec2f8c4d4b8b0b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.787ex; height:6.009ex;" alt="{\displaystyle \int _{-\infty }^{\infty }\,f(t)\ dt\ =\infty }"></span>意思是在<i>f</i>(<i>t</i>)以下的總面積無限大。</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{-\infty }^{\infty }\,f(t)\ dt\ =a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mspace width="thinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>d</mi> <mi>t</mi> <mtext> </mtext> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{-\infty }^{\infty }\,f(t)\ dt\ =a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d90e4eda61c56e25728e6c02c5d43148e7685cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:16.693ex; height:6.009ex;" alt="{\displaystyle \int _{-\infty }^{\infty }\,f(t)\ dt\ =a}"></span>意思是在<i>f</i>(<i>t</i>)以下的總面積是有限的，且總面積等於<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>。</li></ul> <p>無窮大也可以用來描述無窮<a href="/wiki/%E7%BA%A7%E6%95%B0" title="级数">級數</a>： </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=0}^{\infty }\,f(i)=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mspace width="thinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{\infty }\,f(i)=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/105e18f48cc406973adf61572e0e88813f038ed8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:12.348ex; height:6.843ex;" alt="{\displaystyle \sum _{i=0}^{\infty }\,f(i)=a}"></span>意思是無窮級數的和會收斂到某一定值<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>。</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=0}^{\infty }\,f(i)=\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mspace width="thinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{\infty }\,f(i)=\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/621358cfd4ae61960447fe883e38f10bd98b9a95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.442ex; height:6.843ex;" alt="{\displaystyle \sum _{i=0}^{\infty }\,f(i)=\infty }"></span>意思是無窮級數的和會<a href="/wiki/%E5%8F%91%E6%95%A3%E7%BA%A7%E6%95%B0" title="发散级数">发散</a>。</li></ul> <p>若將標記為<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span>和<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span>的點加入到實數組成的拓撲空間，就產生實數集的「兩點<a href="/wiki/%E7%B4%A7%E8%87%B4%E5%8C%96" class="mw-redirect" title="紧致化">緊致化</a>」。再加入代數屬性，就得到了<a href="/wiki/%E6%89%A9%E5%B1%95%E7%9A%84%E5%AE%9E%E6%95%B0%E8%BD%B4" class="mw-redirect" title="扩展的实数轴">扩展的实数轴</a>。也可將<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span>和<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span>作為一個點，記作<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span>，並得到實數的「一點<a href="/wiki/%E7%B4%A7%E8%87%B4%E5%8C%96" class="mw-redirect" title="紧致化">緊致化</a>」，也就是<span class="ilh-all" data-orig-title="實射影線" data-lang-code="en" data-lang-name="英语" data-foreign-title="Real projective line"><span class="ilh-page"><a href="/w/index.php?title=%E5%AF%A6%E5%B0%84%E5%BD%B1%E7%B7%9A&action=edit&redlink=1" class="new" title="實射影線（页面不存在）">實射影線</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Real_projective_line" class="extiw" title="en:Real projective line"><span lang="en" dir="auto">Real projective line</span></a></span><span class="ilh-paren">）</span></span></span>。<a href="/wiki/%E5%B0%84%E5%BD%B1%E5%B9%BE%E4%BD%95" class="mw-redirect" title="射影幾何">射影幾何</a>在平面幾何上引入無窮遠線，在高維上也有類似概念。 </p> <div class="mw-heading mw-heading3"><h3 id="複變分析中的无穷"><span id=".E8.A4.87.E8.AE.8A.E5.88.86.E6.9E.90.E4.B8.AD.E7.9A.84.E6.97.A0.E7.A9.B7"></span>複變分析中的无穷</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=7" title="编辑章节：複變分析中的无穷"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在<a href="/wiki/%E8%A4%87%E8%AE%8A%E5%88%86%E6%9E%90" class="mw-redirect" title="複變分析">複變分析</a>中符號<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span>是指沒有正負號的<a href="/wiki/%E6%9E%81%E9%99%90_(%E6%95%B0%E5%AD%A6)" title="极限 (数学)">极限值</a>。<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\rightarrow \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\rightarrow \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02579e74e2ef1ca0befceba816b311fe5bfd6844" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.268ex; height:1.843ex;" alt="{\displaystyle x\rightarrow \infty }"></span>是指<i>x</i>的大小 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |x|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |x|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4eb41e5fd5dc37eaa1718dfbf4bc082edb991936" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.623ex; height:2.843ex;" alt="{\displaystyle |x|}"></span>會超過任意給定的數值。可以在複數平面上加上<a href="/wiki/%E6%97%A0%E7%A9%B7%E8%BF%9C%E7%82%B9" title="无穷远点">无穷远点</a>，變成一個<a href="/wiki/%E6%8B%93%E6%89%91%E7%A9%BA%E9%97%B4" title="拓扑空间">拓扑空间</a>，即為複數平面的一點<a href="/wiki/%E7%B4%A7%E5%8C%96" title="紧化">紧化</a>。若完成後，所得的平面是一維的<a href="/wiki/%E5%A4%8D%E6%B5%81%E5%BD%A2" title="复流形">复流形</a>或<a href="/wiki/%E9%BB%8E%E6%9B%BC%E6%9B%B2%E9%9D%A2" title="黎曼曲面">黎曼曲面</a>，稱為<a href="/wiki/%E9%BB%8E%E6%9B%BC%E7%90%83%E9%9D%A2" title="黎曼球面">黎曼球面</a>。也可以定義在其上的代數運算（不過有一個例外，無限大不能和本身相加）。另一方面，有無限大表示可以<a href="/wiki/%E9%99%A4%E4%BB%A5%E9%9B%B6" title="除以零">除以零</a>，而對於任何不為0的複數<i>z</i>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {z}{0}}=\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>z</mi> <mn>0</mn> </mfrac> </mrow> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {z}{0}}=\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3b9f1613918d6db79e5292cdca9b9065cee40df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.421ex; height:4.676ex;" alt="{\displaystyle {\frac {z}{0}}=\infty }"></span>，因此可以將<a href="/wiki/%E4%BA%9A%E7%BA%AF%E5%87%BD%E6%95%B0" title="亚纯函数">亚纯函数</a>對映到黎曼球面上，只要將極點對應到无穷远点<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span>即可。複變函數的<a href="/wiki/%E5%AE%9A%E4%B9%89%E5%9F%9F" title="定义域">定義域</a>也可以加入无穷远点，例如<a href="/wiki/%E8%8E%AB%E6%AF%94%E4%B9%8C%E6%96%AF%E5%8F%98%E6%8D%A2" title="莫比乌斯变换">莫比乌斯变换</a>的函數。 </p> <div class="mw-heading mw-heading3"><h3 id="無窮大和無窮小"><span id=".E7.84.A1.E7.AA.AE.E5.A4.A7.E5.92.8C.E7.84.A1.E7.AA.AE.E5.B0.8F"></span>無窮大和無窮小</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=8" title="编辑章节：無窮大和無窮小"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>一般講無窮指的都是<a href="/wiki/%E6%97%A0%E7%A9%B7%E5%A4%A7" class="mw-redirect" title="无穷大">無窮大</a>，但是<a href="/wiki/%E6%97%A0%E7%A9%B7%E5%B0%8F" class="mw-redirect" title="无穷小">無窮小</a>也是一種無窮。通過<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y={\frac {1}{x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y={\frac {1}{x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0871f6114093b98d171970f2974952524b02d1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.42ex; height:5.176ex;" alt="{\displaystyle y={\frac {1}{x}}}"></span>的映射即可把無窮大映射為無窮小。在微積分中，常用高階無窮小的概念。 </p> <div class="mw-heading mw-heading3"><h3 id="無窮遠點"><span id=".E7.84.A1.E7.AA.AE.E9.81.A0.E9.BB.9E"></span>無窮遠點</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=9" title="编辑章节：無窮遠點"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E6%97%A0%E7%A9%B7%E8%BF%9C%E7%82%B9" title="无穷远点">無窮遠點</a>是一個加在實數軸上後得到實射影直線<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} P^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} P^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9252f1ec03073f7c1df976d437a133b8a7c6933a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.554ex; height:2.676ex;" alt="{\displaystyle \mathbb {R} P^{1}}"></span>的點。 </p> <div class="mw-heading mw-heading3"><h3 id="集合論中的無窮"><span id=".E9.9B.86.E5.90.88.E8.AB.96.E4.B8.AD.E7.9A.84.E7.84.A1.E7.AA.AE"></span>集合論中的無窮</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=10" title="编辑章节：集合論中的無窮"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%BA%8F%E6%95%B0" title="序数">序数</a>和<a href="/wiki/%E5%8A%BF%E7%9A%84%E6%AF%94%E8%BE%83" class="mw-redirect" title="势的比较">勢的比較</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif/220px-Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif" decoding="async" width="220" height="115" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif/330px-Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/a/ab/Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif 2x" data-file-width="424" data-file-height="221" /></a><figcaption>無窮集合和其真子集的一對一對應</figcaption></figure> <p>在<a href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" class="mw-redirect" title="集合論">集合論</a>中對無窮有不同的定義。<a href="/wiki/%E5%BE%B7%E5%9C%8B" class="mw-redirect" title="德國">德國</a><a href="/wiki/%E6%95%B8%E5%AD%B8%E5%AE%B6" class="mw-redirect" title="數學家">數學家</a><a href="/wiki/%E5%BA%B7%E6%89%98%E5%B0%94" class="mw-redirect" title="康托尔">康托爾</a>提出，對應於不同<a href="/wiki/%E6%97%A0%E7%A9%B7%E9%9B%86%E5%90%88" class="mw-redirect" title="无穷集合">無窮集合</a>的元素的個數（<a href="/wiki/%E5%9F%BA%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="基数 (数学)">基數</a>），有不同的「無窮」。 </p><p>這裏比較不同的無窮的「大小」的時候，唯一的辦法就是通過是否可以建立「<a href="/wiki/%E4%B8%80%E4%B8%80%E5%B0%8D%E6%87%89" class="mw-redirect" title="一一對應">一一對應</a>關係」來判斷，而拋棄了<a href="/wiki/%E6%AD%90%E5%B9%BE%E9%87%8C%E5%BE%97" class="mw-redirect" title="歐幾里得">歐幾里得</a>「整體大於部分」的看法。例如<a href="/wiki/%E6%95%B4%E6%95%B8%E9%9B%86" class="mw-redirect" title="整數集">整數集</a>和<a href="/wiki/%E8%87%AA%E7%84%B6%E6%95%B8%E9%9B%86" class="mw-redirect" title="自然數集">自然數集</a>由於可以建立一一對應的關係，它們就具有相同的<a href="/wiki/%E5%9F%BA%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="基数 (数学)">基數</a>。 </p><p>例如， </p> <ul><li><a href="/wiki/%E5%8F%AF%E6%95%B0%E9%9B%86%E5%90%88" class="mw-redirect" title="可数集合">可數集合</a>，如<a href="/wiki/%E8%87%AA%E7%84%B6%E6%95%B0" title="自然数">自然數集</a>，<a href="/wiki/%E6%95%B4%E6%95%B0" title="整数">整數集</a>乃至<a href="/wiki/%E6%9C%89%E7%90%86%E6%95%B0" title="有理数">有理數集</a>對應的基數被定義為<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \aleph _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721cd7f8c15a2e72ad162bdfa5baea8eef98aab1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.475ex; height:2.509ex;" alt="{\displaystyle \aleph _{0}}"></span>（阿列夫零）。</li> <li>比<a href="/wiki/%E5%8F%AF%E6%95%B0%E9%9B%86%E5%90%88" class="mw-redirect" title="可数集合">可數集合</a>「大」的稱之為<a href="/wiki/%E4%B8%8D%E5%8F%AF%E6%95%B0%E9%9B%86%E5%90%88" class="mw-redirect" title="不可数集合">不可數集合</a>，如<a href="/wiki/%E5%AE%9E%E6%95%B0%E9%9B%86" class="mw-redirect" title="实数集">實數集</a>，其基數與自然數的冪集相同，為<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{\aleph _{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{\aleph _{0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/779da5db4ed54fa334dd92089cdf1c284e45febb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.231ex; height:2.676ex;" alt="{\displaystyle 2^{\aleph _{0}}}"></span>。</li> <li>由於一個<a href="/wiki/%E6%97%A0%E7%A9%B7%E9%9B%86%E5%90%88" class="mw-redirect" title="无穷集合">無窮集合</a>的冪集總是具有比它本身更高的基數，所以通過構造一系列的冪集，可以證明<a href="/wiki/%E8%B6%85%E7%A9%B7%E5%9F%BA%E6%95%B0" class="mw-redirect" title="超穷基数">超窮基數</a>的個數是無窮的。然而有趣的是，超窮基數的個數比任何基數都多，從而它是一個比任何無窮大都要大的「無窮大」，它不能對應於一個基數，否則會產生某種形式的<a href="/wiki/%E5%BA%B7%E6%89%98%E5%B0%94%E6%82%96%E8%AE%BA" title="康托尔悖论">康托爾悖論</a>。</li></ul> <div class="mw-heading mw-heading3"><h3 id="幾何學和拓扑学"><span id=".E5.B9.BE.E4.BD.95.E5.AD.B8.E5.92.8C.E6.8B.93.E6.89.91.E5.AD.A6"></span>幾何學和拓扑学</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=11" title="编辑章节：幾何學和拓扑学"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4%E7%9A%84%E7%BB%B4%E6%95%B0" title="向量空间的维数">向量空間的維數</a></div> <p>無限<a href="/wiki/%E7%B6%AD%E6%95%B8" class="mw-redirect" title="維數">維</a>的空間常用在<a href="/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" class="mw-redirect" title="幾何學">幾何學</a>及<a href="/wiki/%E6%8B%93%E6%89%91%E5%AD%A6" title="拓扑学">拓扑学</a>中，尤其是在<span class="ilh-all" data-orig-title="分類空間" data-lang-code="en" data-lang-name="英语" data-foreign-title="classifying space"><span class="ilh-page"><a href="/w/index.php?title=%E5%88%86%E9%A1%9E%E7%A9%BA%E9%96%93&action=edit&redlink=1" class="new" title="分類空間（页面不存在）">分類空間</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/classifying_space" class="extiw" title="en:classifying space"><span lang="en" dir="auto">classifying space</span></a></span><span class="ilh-paren">）</span></span></span>，也就是<span class="ilh-all" data-orig-title="Eilenberg−MacLane空間" data-lang-code="en" data-lang-name="英语" data-foreign-title="Eilenberg−MacLane space"><span class="ilh-page"><a href="/w/index.php?title=Eilenberg%E2%88%92MacLane%E7%A9%BA%E9%96%93&action=edit&redlink=1" class="new" title="Eilenberg−MacLane空間（页面不存在）">Eilenberg−MacLane空間</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Eilenberg%E2%88%92MacLane_space" class="extiw" title="en:Eilenberg−MacLane space"><span lang="en" dir="auto">Eilenberg−MacLane space</span></a></span><span class="ilh-paren">）</span></span></span>。常見的例子包括無限維的<span class="ilh-all" data-orig-title="複射影空間" data-lang-code="en" data-lang-name="英语" data-foreign-title="complex projective space"><span class="ilh-page"><a href="/w/index.php?title=%E8%A4%87%E5%B0%84%E5%BD%B1%E7%A9%BA%E9%96%93&action=edit&redlink=1" class="new" title="複射影空間（页面不存在）">複射影空間</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/complex_projective_space" class="extiw" title="en:complex projective space"><span lang="en" dir="auto">complex projective space</span></a></span><span class="ilh-paren">）</span></span></span>K(Z,2)，以及無限維的<a href="/wiki/%E5%AE%9E%E5%B0%84%E5%BD%B1%E7%A9%BA%E9%97%B4" title="实射影空间">實射影空間</a>K(Z/2Z,1)。 </p> <div class="mw-heading mw-heading3"><h3 id="分形"><span id=".E5.88.86.E5.BD.A2"></span>分形</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=12" title="编辑章节：分形"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:KochFlake.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/KochFlake.svg/140px-KochFlake.svg.png" decoding="async" width="140" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/KochFlake.svg/210px-KochFlake.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/KochFlake.svg/280px-KochFlake.svg.png 2x" data-file-width="362" data-file-height="362" /></a><figcaption>科赫曲線的前四次迭代</figcaption></figure> <p><a href="/wiki/%E5%88%86%E5%BD%A2" title="分形">分形</a>的結構可以重覆的放大，分形可以無限次的放大，但不會變的圓滑，而且仍維持原有的結構，分形的周長是無限的，有些的面積無限，但有些的面積卻是有限。像<a href="/wiki/%E7%A7%91%E8%B5%AB%E6%9B%B2%E7%B7%9A" title="科赫曲線">科赫曲線</a>就是有無限周長和有限面積的例子。 </p> <div class="mw-heading mw-heading3"><h3 id="沒有無窮的數學"><span id=".E6.B2.92.E6.9C.89.E7.84.A1.E7.AA.AE.E7.9A.84.E6.95.B8.E5.AD.B8"></span>沒有無窮的數學</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=13" title="编辑章节：沒有無窮的數學"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E5%88%A9%E5%A5%A5%E6%B3%A2%E5%BE%B7%C2%B7%E5%85%8B%E7%BD%97%E5%86%85%E5%85%8B" title="利奥波德·克罗内克">利奧波德·克羅內克</a>懷疑無限的概念，也懷疑1870年代及1880年代時數學家使用無限的方式。這種懷疑主義形成一種稱為<a href="/wiki/%E6%9C%89%E9%99%90%E4%B8%BB%E7%BE%A9" title="有限主義">有限主義</a>的<a href="/wiki/%E6%95%B8%E5%AD%B8%E5%93%B2%E5%AD%B8" class="mw-redirect" title="數學哲學">數學哲學</a>，是屬於<a href="/wiki/%E6%95%B0%E5%AD%A6%E7%BB%93%E6%9E%84%E4%B8%BB%E4%B9%89" class="mw-redirect" title="数学结构主义">數學結構主義</a>及<a href="/wiki/%E6%95%B0%E5%AD%A6%E7%9B%B4%E8%A7%89%E4%B8%BB%E4%B9%89" class="mw-redirect" title="数学直觉主义">數學直覺主義</a>中的一種極端形式<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="物理中的無窮"><span id=".E7.89.A9.E7.90.86.E4.B8.AD.E7.9A.84.E7.84.A1.E7.AA.AE"></span>物理中的無窮</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=14" title="编辑章节：物理中的無窮"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在物理上，實數的近似會用在<span class="ilh-all" data-orig-title="連續量 (量測)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Continuum (theory)"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%A3%E7%BA%8C%E9%87%8F_(%E9%87%8F%E6%B8%AC)&action=edit&redlink=1" class="new" title="連續量 (量測)（页面不存在）">連續量</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Continuum_(theory)" class="extiw" title="en:Continuum (theory)"><span lang="en" dir="auto">Continuum (theory)</span></a></span><span class="ilh-paren">）</span></span></span>的量測上，自然數的近似會用在<a href="/wiki/%E9%9B%A2%E6%95%A3" class="mw-disambig" title="離散">離散</a>的量測上。因此科學家假設沒有可觀察量會到無窮的數值<style data-mw-deduplicate="TemplateStyles:r83946278">.mw-parser-output .template-facttext{background-color:var(--background-color-neutral,#eaecf0);color:inherit;margin:-.3em 0;padding:.3em 0}</style><sup class="noprint Template-Fact"><a href="/wiki/Wikipedia:%E5%88%97%E6%98%8E%E6%9D%A5%E6%BA%90" title="Wikipedia:列明来源"><span style="white-space: nowrap;" title="来源请求。">[來源請求]</span></a></sup>，这是因为科学家很自然的，事实上已经是默认的接受了这样的事情：即在真实的物理场景里，是不存无穷大的可观测物理量的。例如在<a href="/wiki/%E6%89%A9%E5%B1%95%E7%9A%84%E5%AE%9E%E6%95%B0%E8%BD%B4" class="mw-redirect" title="扩展的实数轴">擴展的實數軸</a>上取一個無窮的值，或是需要計算某個無窮次事件的次數。因此會預設沒有任何物體會有無窮的質量或是能量。有些事物的概念和無限有關，例如無限<a href="/wiki/%E5%B9%B3%E9%9D%A2%E6%B3%A2" title="平面波">平面波</a>，但現今尚沒有方法可以由實驗產生無限平面波<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="電腦計算中的無窮"><span id=".E9.9B.BB.E8.85.A6.E8.A8.88.E7.AE.97.E4.B8.AD.E7.9A.84.E7.84.A1.E7.AA.AE"></span>電腦計算中的無窮</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=15" title="编辑章节：電腦計算中的無窮"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/IEEE_754" title="IEEE 754">IEEE 754</a><a href="/wiki/%E6%B5%AE%E9%BB%9E%E6%95%B8" class="mw-redirect" title="浮點數">浮點數</a>標準中定義了正無限大及負無限大，定義為<a href="/wiki/%E7%AE%97%E8%A1%93%E6%BA%A2%E4%BD%8D" class="mw-redirect" title="算術溢位">溢位</a>、<a href="/wiki/%E9%99%A4%E4%BB%A5%E9%9B%B6" title="除以零">除以零</a>或其他異常程序的結果。 </p><p>像<a href="/wiki/Java" title="Java">Java</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>及<a href="/wiki/J%E8%AA%9E%E8%A8%80" class="mw-redirect" title="J語言">J語言</a><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>等<a href="/wiki/%E7%A8%8B%E5%BC%8F%E8%AA%9E%E8%A8%80" class="mw-redirect" title="程式語言">程式語言</a>允許在程式中直接用類似常數的方式存取正負無限大。正負無限大可以作為<a href="/wiki/%E6%9C%80%E5%A4%A7%E5%85%83" class="mw-redirect" title="最大元">最大元</a>，因為比所有其他的數都大（或是小）。正負無限大也可以做為像<a href="/wiki/%E6%8E%92%E5%BA%8F" class="mw-redirect" title="排序">排序</a>、<a href="/wiki/%E6%90%9C%E5%AF%BB" class="mw-redirect" title="搜寻">搜尋</a>或<a href="/wiki/%E7%AA%97%E5%87%BD%E6%95%B0" title="窗函数">窗函数</a>等<a href="/wiki/%E6%BC%94%E7%AE%97%E6%B3%95" class="mw-redirect" title="演算法">演算法</a>中的<span class="ilh-all" data-orig-title="哨兵值" data-lang-code="en" data-lang-name="英语" data-foreign-title="sentinel value"><span class="ilh-page"><a href="/w/index.php?title=%E5%93%A8%E5%85%B5%E5%80%BC&action=edit&redlink=1" class="new" title="哨兵值（页面不存在）">哨兵值</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/sentinel_value" class="extiw" title="en:sentinel value"><span lang="en" dir="auto">sentinel value</span></a></span><span class="ilh-paren">）</span></span></span>，找到這個值時可以結束計算。 </p><p>在一些沒有最大或最小元素，但允許<a href="/wiki/%E9%97%9C%E4%BF%82%E9%81%8B%E7%AE%97%E5%AD%90" title="關係運算子">關係運算子</a><a href="/wiki/%E9%81%8B%E7%AE%97%E5%AD%90%E5%A4%9A%E8%BC%89" class="mw-redirect" title="運算子多載">多載</a>的程式語言中，程式設計師也可以「創建」最大及最小元素。若語言不允許直接存取最大或最小元素，但有<a href="/wiki/%E6%B5%AE%E9%BB%9E%E6%95%B8" class="mw-redirect" title="浮點數">浮點數</a>的形態，也可以用特定的運算產生正負無限大，再進行其他處理。 </p><p><a href="/wiki/%E5%BE%AE%E8%BD%AF" title="微软">微软</a>的 <a href="/wiki/Visual_Studio" class="mw-redirect" title="Visual Studio">Visual Studio</a> 用无穷大符号作为<a href="/wiki/%E6%A0%87%E5%BF%97" title="标志">图标</a>。 </p> <div class="mw-heading mw-heading2"><h2 id="藝術及認知科學中的无穷"><span id=".E8.97.9D.E8.A1.93.E5.8F.8A.E8.AA.8D.E7.9F.A5.E7.A7.91.E5.AD.B8.E4.B8.AD.E7.9A.84.E6.97.A0.E7.A9.B7"></span>藝術及認知科學中的无穷</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=16" title="编辑章节：藝術及認知科學中的无穷"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E9%80%8F%E8%A7%86%E6%8A%95%E5%BD%B1" title="透视投影">透视</a>藝術使用了<a href="/wiki/%E6%B6%88%E5%A4%B1%E7%82%B9" title="消失点">消失点</a>或是<a href="/wiki/%E6%97%A0%E7%A9%B7%E8%BF%9C%E7%82%B9" title="无穷远点">無窮遠點</a>的概念．也就是放在觀察者無窮遠處的一個點。因此畫家可以繪製有現實感空間及距離的作品<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>。藝術家<a href="/wiki/%E8%8E%AB%E9%87%8C%E8%8C%A8%C2%B7%E7%A7%91%E5%86%85%E5%88%A9%E6%96%AF%C2%B7%E5%9F%83%E8%88%8D%E5%B0%94" title="莫里茨·科内利斯·埃舍尔">莫里茨·科内利斯·埃舍尔</a>就常將無窮的概念用在他的作品中。 </p><p><a href="/wiki/%E8%AA%8D%E7%9F%A5%E7%A7%91%E5%AD%B8" class="mw-redirect" title="認知科學">認知科學家</a><a href="/wiki/%E5%96%AC%E6%B2%BB%C2%B7%E8%90%8A%E8%80%83%E5%A4%AB" title="喬治·萊考夫">喬治·萊考夫</a>將數學及科學中無限的概念視為一個隱喻。這個觀點是基於簡單的無限隱喻，定義為一直遞增的數列<1,2,3,...>。 </p><p>無限的符號常浪漫的表示永恆的愛，許多現代的珠寶就在其造型中加入無限的符號。 </p><p><a href="/wiki/Crypton_Future_Media" class="mw-redirect" title="Crypton Future Media">Crypton Future Media</a> 的<a href="/wiki/%E8%A7%92%E8%89%B2%E4%B8%BB%E5%94%B1%E7%B3%BB%E5%88%97" title="角色主唱系列">角色主唱系列</a>中 CV-03 <a href="/wiki/%E5%B7%A1%E9%9F%B3%E6%B5%81%E6%AD%8C" title="巡音流歌">巡音流歌</a>的人物形象即包含无穷大的符号以象征“循环、巡回”之意。 </p> <div class="mw-heading mw-heading2"><h2 id="相關條目"><span id=".E7.9B.B8.E9.97.9C.E6.A2.9D.E7.9B.AE"></span>相關條目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=17" title="编辑章节：相關條目"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/0.999%E2%80%A6" title="0.999…">0.999…</a></li> <li><a href="/wiki/%E9%9D%9E%E6%A0%87%E5%87%86%E5%88%86%E6%9E%90" title="非标准分析">非標准分析</a></li> <li><a href="/wiki/%E9%80%A3%E7%BA%8C%E7%B5%B1%E5%81%87%E8%A8%AD" class="mw-redirect" title="連續統假設">連續統假設</a></li> <li><a href="/wiki/%E7%84%A1%E9%99%90%E7%8C%B4%E5%AD%90%E5%AE%9A%E7%90%86" title="無限猴子定理">無限猴子定理</a></li> <li><a href="/wiki/%E7%84%A1%E7%AA%AE%E5%85%AC%E7%90%86" class="mw-redirect" title="無窮公理">無窮公理</a></li> <li><a href="/wiki/%E9%8A%9C%E5%B0%BE%E8%9B%87" title="銜尾蛇">銜尾蛇</a></li> <li><a href="/wiki/%E8%89%BE%E7%A6%AE%E5%AF%8C%E6%95%B8" class="mw-redirect" title="艾禮富數">艾禮富數</a></li> <li><a href="/wiki/%E6%97%A0%E9%99%90%E9%9B%86%E5%90%88" title="无限集合">无限集合</a></li> <li><a href="/wiki/%E8%B6%85%E7%8F%BE%E5%AF%A6%E6%95%B8" title="超現實數">超現實數</a></li> <li><a href="/wiki/%E7%84%A1%E7%AA%AE%E9%81%A0%E7%84%A6%E9%BB%9E" title="無窮遠焦點">無窮遠焦點</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="參考資料"><span id=".E5.8F.83.E8.80.83.E8.B3.87.E6.96.99"></span>參考資料</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%97%A0%E7%A9%B7&action=edit&section=18" title="编辑章节：參考資料"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite id="CITEREFScott1981" class="citation">Scott, Joseph Frederick, <a rel="nofollow" class="external text" href="http://books.google.com/books?id=XX9PKytw8g8C&pg=PA24">The mathematical work of John Wallis, D.D., F.R.S., (1616–1703)</a> 2, American Mathematical Society: 24, 1981 <span class="reference-accessdate"> [<span class="nowrap">2014-10-17</span>]</span>, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-8284-0314-7" title="Special:网络书源/0-8284-0314-7"><span title="国际标准书号">ISBN</span> 0-8284-0314-7</a>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20210304082900/https://books.google.com/books?id=XX9PKytw8g8C&pg=PA24">存档</a>于2021-03-04）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.aufirst=Joseph+Frederick&rft.aulast=Scott&rft.btitle=The+mathematical+work+of+John+Wallis%2C+D.D.%2C+F.R.S.%2C+%281616%E2%80%931703%29&rft.date=1981&rft.edition=2&rft.genre=book&rft.isbn=0-8284-0314-7&rft.pages=24&rft.pub=American+Mathematical+Society&rft_id=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DXX9PKytw8g8C%26pg%3DPA24&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFMartin-Löf1990" class="citation"><a href="/wiki/Per_Martin-L%C3%B6f" class="mw-redirect" title="Per Martin-Löf">Martin-Löf, Per</a>, Mathematics of infinity, COLOG-88 (Tallinn, 1988), Lecture Notes in Computer Science <b>417</b>, Berlin: Springer: 146–197, 1990, <a rel="nofollow" class="external text" href="//www.ams.org/mathscinet-getitem?mr=1064143"><span title="數學評論">MR 1064143</span></a>, <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-52335-9_54"><span title="數位物件識別號">doi:10.1007/3-540-52335-9_54</span></a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.atitle=Mathematics+of+infinity&rft.aufirst=Per&rft.aulast=Martin-L%C3%B6f&rft.btitle=COLOG-88+%28Tallinn%2C+1988%29&rft.date=1990&rft.genre=bookitem&rft.pages=146-197&rft.place=Berlin&rft.pub=Springer&rft.series=Lecture+Notes+in+Computer+Science&rft_id=%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D1064143&rft_id=info%3Adoi%2F10.1007%2F3-540-52335-9_54&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFO'Flaherty1986" class="citation">O'Flaherty, Wendy Doniger, <a rel="nofollow" class="external text" href="http://books.google.com/books?id=vhNNrX3bmo4C&pg=PA243">Dreams, Illusion, and Other Realities</a>, University of Chicago Press: 243, 1986 <span class="reference-accessdate"> [<span class="nowrap">2014-10-17</span>]</span>, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780226618555" title="Special:网络书源/9780226618555"><span title="国际标准书号">ISBN</span> 9780226618555</a>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20200818203714/https://books.google.com/books?id=vhNNrX3bmo4C&pg=PA243">存档</a>于2020-08-18）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.aufirst=Wendy+Doniger&rft.aulast=O%27Flaherty&rft.btitle=Dreams%2C+Illusion%2C+and+Other+Realities&rft.date=1986&rft.genre=book&rft.isbn=9780226618555&rft.pages=243&rft.pub=University+of+Chicago+Press&rft_id=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DvhNNrX3bmo4C%26pg%3DPA243&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFToker1989" class="citation">Toker, Leona, <a rel="nofollow" class="external text" href="http://books.google.com/books?id=Jud1q_NrqpcC&pg=PA159">Nabokov: The Mystery of Literary Structures</a>, Cornell University Press: 159, 1989 <span class="reference-accessdate"> [<span class="nowrap">2014-10-17</span>]</span>, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780801422119" title="Special:网络书源/9780801422119"><span title="国际标准书号">ISBN</span> 9780801422119</a>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20200803091121/https://books.google.com/books?id=Jud1q_NrqpcC&pg=PA159">存档</a>于2020-08-03）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.aufirst=Leona&rft.aulast=Toker&rft.btitle=Nabokov%3A+The+Mystery+of+Literary+Structures&rft.date=1989&rft.genre=book&rft.isbn=9780801422119&rft.pages=159&rft.pub=Cornell+University+Press&rft_id=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DJud1q_NrqpcC%26pg%3DPA159&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/continuity">Continuity and Infinitesimals entry by John Lane Bell in the <i>Stanford Encyclopedia of Philosophy</i></a>. <span class="reference-accessdate"> [<span class="nowrap">2014-10-18</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20210125184359/https://plato.stanford.edu/entries/continuity/">存档</a>于2021-01-25）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.btitle=Continuity+and+Infinitesimals+entry+by+John+Lane+Bell+in+the+Stanford+Encyclopedia+of+Philosophy&rft.genre=unknown&rft_id=http%3A%2F%2Fplato.stanford.edu%2Fentries%2Fcontinuity&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation journal">Jesseph, Douglas Michael. <a rel="nofollow" class="external text" href="http://muse.jhu.edu/journals/perspectives_on_science/v006/6.1jesseph.html">Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes</a>. <a href="/w/index.php?title=Perspectives_on_Science&action=edit&redlink=1" class="new" title="Perspectives on Science（页面不存在）">Perspectives on Science</a>. 1998, <b>6</b> (1&2): 6–40 <span class="reference-accessdate"> [<span class="nowrap">16 February</span> 2010]</span>. <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/1063-6145"><span title="国际标准连续出版物号">ISSN 1063-6145</span></a>. <a rel="nofollow" class="external text" href="//www.worldcat.org/oclc/42413222"><span title="OCLC">OCLC 42413222</span></a>. （原始内容<a rel="nofollow" class="external text" href="https://www.webcitation.org/5nZWht6FE?url=http://muse.jhu.edu/journals/perspectives_on_science/v006/6.1jesseph.html">存档</a>于2010-02-15）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.atitle=Leibniz+on+the+Foundations+of+the+Calculus%3A+The+Question+of+the+Reality+of+Infinitesimal+Magnitudes&rft.aufirst=Douglas+Michael&rft.aulast=Jesseph&rft.date=1998&rft.genre=article&rft.issn=1063-6145&rft.issue=1%262&rft.jtitle=Perspectives+on+Science&rft.pages=6-40&rft.volume=6&rft_id=http%3A%2F%2Fmuse.jhu.edu%2Fjournals%2Fperspectives_on_science%2Fv006%2F6.1jesseph.html&rft_id=info%3Aoclcnum%2F42413222&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">這類在積分及級數中使用無限大的例子在任一本標準的微積分教科書中都可以找到，例如<a href="#CITEREFSwokoski1983">Swokoski 1983</a>，pp. 468-510<span class="error harv-error" style="display: none; font-size:100%"> harvnb模板錯誤: 無指向目標: CITEREFSwokoski1983 (<a href="/wiki/Category:%E5%90%AB%E6%9C%89%E5%93%88%E4%BD%9B%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE%E6%A0%BC%E5%BC%8F%E7%B3%BB%E5%88%97%E6%A8%A1%E6%9D%BF%E9%93%BE%E6%8E%A5%E6%8C%87%E5%90%91%E9%94%99%E8%AF%AF%E7%9A%84%E9%A1%B5%E9%9D%A2" title="Category:含有哈佛参考文献格式系列模板链接指向错误的页面">幫助</a>)</span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite class="citation book"><a href="/w/index.php?title=Morris_Kline&action=edit&redlink=1" class="new" title="Morris Kline（页面不存在）">Kline, Morris</a>. <a rel="nofollow" class="external text" href="https://archive.org/details/mathematicalthou00klin">Mathematical Thought from Ancient to Modern Times</a>. New York: Oxford University Press. 1972: 1197–1198. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-19-506135-7" title="Special:网络书源/0-19-506135-7"><span title="国际标准书号">ISBN</span> 0-19-506135-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.aufirst=Morris&rft.aulast=Kline&rft.btitle=Mathematical+Thought+from+Ancient+to+Modern+Times&rft.date=1972&rft.genre=book&rft.isbn=0-19-506135-7&rft.pages=1197-1198&rft.place=New+York&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmathematicalthou00klin&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.doriclenses.com/administrer/upload/pdf/NOT_AXI_ENG_070212_doricl97_doricle_kvgwQP.pdf">Doric Lenses</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20130124011604/http://www.doriclenses.com/administrer/upload/pdf/NOT_AXI_ENG_070212_doricl97_doricle_kvgwQP.pdf">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） - Application Note - Axicons - 2. Intensity Distribution. Retrieved 7 April 2014.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite class="citation book">Gosling, James; et. al. 4.2.3.. <a rel="nofollow" class="external text" href="http://docs.oracle.com/javase/specs/jls/se7/html/jls-4.html#jls-4.2.3">The Java™ Language Specification</a> Java SE 7. California, U.S.A.: Oracle America, Inc. 27 July 2012 <span class="reference-accessdate"> [<span class="nowrap">6 September</span> 2012]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20120609071157/http://docs.oracle.com/javase/specs/jls/se7/html/jls-4.html#jls-4.2.3">存档</a>于2012-06-09）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.atitle=4.2.3.&rft.au=et.+al.&rft.aufirst=James&rft.aulast=Gosling&rft.btitle=The+Java%E2%84%A2+Language+Specification&rft.date=2012-07-27&rft.edition=Java+SE+7&rft.genre=bookitem&rft.place=California%2C+U.S.A.&rft.pub=Oracle+America%2C+Inc.&rft_id=http%3A%2F%2Fdocs.oracle.com%2Fjavase%2Fspecs%2Fjls%2Fse7%2Fhtml%2Fjls-4.html%23jls-4.2.3&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite class="citation book">Stokes, Roger. 19.2.1. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120325064205/http://www.rogerstokes.free-online.co.uk/19.htm#10">Learning J</a>. July 2012 <span class="reference-accessdate"> [<span class="nowrap">6 September</span> 2012]</span>. （<a rel="nofollow" class="external text" href="http://www.rogerstokes.free-online.co.uk/19.htm#10">原始内容</a>存档于2012-03-25）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.atitle=19.2.1&rft.aufirst=Roger&rft.aulast=Stokes&rft.btitle=Learning+J&rft.date=2012-07&rft.genre=bookitem&rft_id=http%3A%2F%2Fwww.rogerstokes.free-online.co.uk%2F19.htm%2310&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite class="citation book">Kline, Morris. <a rel="nofollow" class="external text" href="http://books.google.com/books?id=f-e0bro-0FUC&pg=PA229">Mathematics for the nonmathematician</a>. Courier Dover Publications. 1985: 229 <span class="reference-accessdate"> [<span class="nowrap">2014-10-17</span>]</span>. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-486-24823-2" title="Special:网络书源/0-486-24823-2"><span title="国际标准书号">ISBN</span> 0-486-24823-2</a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20200803113806/https://books.google.com/books?id=f-e0bro-0FUC&pg=PA229">存档</a>于2020-08-03）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%97%A0%E7%A9%B7&rft.aufirst=Morris&rft.aulast=Kline&rft.btitle=Mathematics+for+the+nonmathematician&rft.date=1985&rft.genre=book&rft.isbn=0-486-24823-2&rft.pages=229&rft.pub=Courier+Dover+Publications&rft_id=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Df-e0bro-0FUC%26pg%3DPA229&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span>, <a rel="nofollow" class="external text" href="http://books.google.com/books?id=f-e0bro-0FUC&pg=PA229">Section 10-7, p. 229</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20200803113806/http://books.google.com/books?id=f-e0bro-0FUC&pg=PA229">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</span> </li> </ol></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84261037">.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 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.navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em;width:auto;padding-left:0.2em;position:absolute;left:1em}.mw-parser-output .navbox .mw-collapsible-toggle{margin-left:0.5em;position:absolute;right:1em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="大数" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E5%A4%A7%E6%95%B0" title="Template:大数"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E5%A4%A7%E6%95%B0" title="Template talk:大数"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E5%A4%A7%E6%95%B0" title="Special:编辑页面/Template:大数"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="大数" style="font-size:110%;margin:0 5em"><a href="/wiki/%E5%A4%A7%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="大数 (数学)">大数</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">范例（按数字大小排列）</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%8F%A4%E6%88%88%E7%88%BE" title="古戈爾">古戈爾</a> · <span class="nowrap"><a href="/wiki/%E5%8F%A4%E6%88%88%E7%88%BE%E6%99%AE%E5%8B%92%E5%85%8B%E6%96%AF" title="古戈爾普勒克斯">古戈尔普勒克斯</a> ·</span> <span class="nowrap"><a href="/wiki/%E6%96%AF%E5%A5%8E%E6%96%AF%E6%95%B0" title="斯奎斯数">斯奎斯数</a> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="古戈爾普勒克斯普勒克斯" data-lang-code="en" data-lang-name="英语" data-foreign-title="Googolplexplex"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E6%88%88%E7%88%BE%E6%99%AE%E5%8B%92%E5%85%8B%E6%96%AF%E6%99%AE%E5%8B%92%E5%85%8B%E6%96%AF&action=edit&redlink=1" class="new" title="古戈爾普勒克斯普勒克斯（页面不存在）">古戈爾普勒克斯普勒克斯</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Googolplexplex" class="extiw" title="en:Googolplexplex"><span lang="en" dir="auto">Googolplexplex</span></a></span><span class="ilh-paren">）</span></span></span> ·</span> <span class="nowrap"><a href="/wiki/%E6%96%AF%E5%9D%A6%E8%B1%AA%E6%96%AF-%E8%8E%AB%E6%BE%A4%E8%A1%A8%E7%A4%BA%E6%B3%95#莫澤數" title="斯坦豪斯-莫澤表示法">莫澤數</a> ·</span> <span class="nowrap"><a href="/wiki/%E8%91%9B%E7%AB%8B%E6%81%86%E6%95%B8" title="葛立恆數">葛立恆數</a> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="TREE(3)" data-lang-code="en" data-lang-name="英语" data-foreign-title="TREE(3)"><span class="ilh-page"><a href="/w/index.php?title=TREE(3)&action=edit&redlink=1" class="new" title="TREE(3)（页面不存在）">TREE(3)</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/TREE(3)" class="extiw" title="en:TREE(3)"><span lang="en" dir="auto">TREE(3)</span></a></span><span class="ilh-paren">）</span></span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="SSCG(3)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Friedman’s SSCG function"><span class="ilh-page"><a href="/w/index.php?title=SSCG(3)&action=edit&redlink=1" class="new" title="SSCG(3)（页面不存在）">SSCG(3)</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Friedman%E2%80%99s_SSCG_function" class="extiw" title="en:Friedman’s SSCG function"><span lang="en" dir="auto">Friedman’s SSCG function</span></a></span><span class="ilh-paren">）</span></span></span> ·</span> <span class="nowrap"><a href="/wiki/%E6%8B%89%E7%B4%84%E6%95%B8" title="拉約數">拉約數</a> ·</span> <span class="nowrap"><a href="/wiki/%E8%B6%85%E9%99%90%E6%95%B0" title="超限数">超限数</a> ·</span> <span class="nowrap"><a class="mw-selflink selflink"><big>∞</big></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">表达方法</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">记号</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%AB%98%E5%BE%B7%E7%B4%8D%E7%AE%AD%E8%99%9F%E8%A1%A8%E7%A4%BA%E6%B3%95" title="高德納箭號表示法">高德納箭號表示法</a> · <span class="nowrap"><a href="/wiki/%E5%BA%B7%E5%A8%81%E9%8F%88%E5%BC%8F%E7%AE%AD%E8%99%9F%E8%A1%A8%E7%A4%BA%E6%B3%95" title="康威鏈式箭號表示法">康威鏈式箭號表示法</a> ·</span> <span class="nowrap"><a href="/wiki/%E6%96%AF%E5%9D%A6%E8%B1%AA%E6%96%AF-%E8%8E%AB%E6%BE%A4%E8%A1%A8%E7%A4%BA%E6%B3%95" title="斯坦豪斯-莫澤表示法">斯坦豪斯-莫澤表示法</a> ·</span> <span class="nowrap"><a href="/wiki/%E6%80%A5%E6%88%90%E9%95%BF%E9%98%B6%E5%B1%82" title="急成长阶层">急成长阶层</a> ·</span> <span class="nowrap"><a href="/wiki/%E7%BC%93%E6%88%90%E9%95%BF%E9%98%B6%E5%B1%82" title="缓成长阶层">缓成长阶层</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">运算  </th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E8%B6%85%E8%BF%90%E7%AE%97" title="超运算">超运算</a>（<a href="/wiki/%E8%BF%AD%E4%BB%A3%E5%86%AA%E6%AC%A1" title="迭代冪次">迭代冪次</a> · <span class="nowrap"><a href="/wiki/%E4%BA%94%E7%BA%A7%E8%BF%90%E7%AE%97" title="五级运算">五級運算</a>） ·</span> <span class="nowrap"><a href="/wiki/%E9%98%BF%E5%85%8B%E6%9B%BC%E5%87%BD%E6%95%B8" title="阿克曼函數">阿克曼函數</a></span></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">相关条目</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E7%84%A1%E7%AA%AE%E5%B0%8F%E9%87%8F" title="無窮小量">無窮小量</a> · <span class="nowrap"><a href="/wiki/%E6%95%B8%E7%B3%BB" title="數系">数系</a> ·</span> <span class="nowrap"><a href="/wiki/%E6%95%B8%E8%A9%9E" title="數詞">數詞</a> ·</span> <span class="nowrap"><a href="/wiki/%E6%95%B0%E9%87%8F%E7%BA%A7_(%E6%95%B0)" title="数量级 (数)">数量级</a> ·</span> <span class="nowrap"><a href="/wiki/%E6%95%B8%E8%A1%A8" title="數表">數表</a> ·</span> <span class="nowrap"> <a href="/wiki/%E4%B8%8D%E7%A2%BA%E5%AE%9A%E6%95%B8%E5%AD%97%E5%92%8C%E8%99%9B%E6%93%AC%E6%95%B8%E5%AD%97" class="mw-redirect" title="不確定數字和虛擬數字">不確定數字和虛擬數字</a> ·</span> <span class="nowrap"><a href="/wiki/%E6%93%B4%E5%B1%95%E5%AF%A6%E6%95%B8%E7%B7%9A" title="擴展實數線">擴展實數線</a> ·</span> <span class="nowrap"><a href="/wiki/2%E7%9A%84%E5%B9%82" title="2的幂">2的冪</a> ·</span> <span class="nowrap"><a href="/wiki/10%E7%9A%84%E5%B9%82" title="10的幂">10的冪</a> ·</span> <span class="nowrap"><a href="/wiki/%E8%A5%BF%E6%96%B9%E7%9A%84%E6%95%B0%E5%AD%97%E5%91%BD%E5%90%8D%E6%B3%95" title="西方的数字命名法">西方的數字命名法</a> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="泰坦質數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Titanic prime"><span class="ilh-page"><a href="/w/index.php?title=%E6%B3%B0%E5%9D%A6%E8%B3%AA%E6%95%B8&action=edit&redlink=1" class="new" title="泰坦質數（页面不存在）">泰坦質數</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Titanic_prime" class="extiw" title="en:Titanic prime"><span lang="en" dir="auto">Titanic prime</span></a></span><span class="ilh-paren">）</span></span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="吉甘質數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Gigantic prime"><span class="ilh-page"><a href="/w/index.php?title=%E5%90%89%E7%94%98%E8%B3%AA%E6%95%B8&action=edit&redlink=1" class="new" title="吉甘質數（页面不存在）">吉甘質數</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Gigantic_prime" class="extiw" title="en:Gigantic prime"><span lang="en" dir="auto">Gigantic prime</span></a></span><span class="ilh-paren">）</span></span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="麥咖質數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Megaprime"><span class="ilh-page"><a href="/w/index.php?title=%E9%BA%A5%E5%92%96%E8%B3%AA%E6%95%B8&action=edit&redlink=1" class="new" title="麥咖質數（页面不存在）">麥咖質數</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Megaprime" class="extiw" title="en:Megaprime"><span lang="en" dir="auto">Megaprime</span></a></span><span class="ilh-paren">）</span></span></span> ·</span> <span class="nowrap"><a href="/wiki/%E5%B7%B2%E7%9F%A5%E6%9C%80%E5%A4%A7%E8%B3%AA%E6%95%B8" title="已知最大質數">已知最大質數</a></span></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><span class="ilh-all" data-orig-title="大數的名字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Names of large numbers"><span class="ilh-page"><a href="/w/index.php?title=%E5%A4%A7%E6%95%B8%E7%9A%84%E5%90%8D%E5%AD%97&action=edit&redlink=1" class="new" title="大數的名字（页面不存在）">名字</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Names_of_large_numbers" class="extiw" title="en:Names of large numbers"><span lang="en" dir="auto">Names of large numbers</span></a></span><span class="ilh-paren">）</span></span></span> · <span class="nowrap"><span class="ilh-all" data-orig-title="大数的历史" data-lang-code="en" data-lang-name="英语" data-foreign-title="History of large numbers"><span class="ilh-page"><a href="/w/index.php?title=%E5%A4%A7%E6%95%B0%E7%9A%84%E5%8E%86%E5%8F%B2&action=edit&redlink=1" class="new" title="大数的历史（页面不存在）">歷史</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/History_of_large_numbers" class="extiw" title="en:History of large numbers"><span lang="en" dir="auto">History of large numbers</span></a></span><span class="ilh-paren">）</span></span></span></span></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"></div><div role="navigation" class="navbox" aria-labelledby="無限_∞" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="3" style="background:#AB23CB; color:#FEFEFE"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E7%84%A1%E9%99%90" title="Template:無限"><abbr title="查看该模板" style="color:#FEFEFE">查</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:%E7%84%A1%E9%99%90&action=edit&redlink=1" class="new" title="Template talk:無限（页面不存在）"><abbr title="讨论该模板" style="color:#FEFEFE">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E7%84%A1%E9%99%90" title="Special:编辑页面/Template:無限"><abbr title="编辑该模板" style="color:#FEFEFE">编</abbr></a></li></ul></div><div id="無限_∞" style="font-size:110%;margin:0 5em"><a class="mw-selflink selflink"><span style="color:white">無限</span></a> ∞</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#BB33DD; color:#FEFEFE">歷史</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%BA%B7%E6%89%98%E5%B0%94%E6%82%96%E8%AE%BA" title="康托尔悖论">康托爾悖論</a></li> <li><span class="ilh-all" data-orig-title="Controversy over Cantor's theory" data-lang-code="en" data-lang-name="英语" data-foreign-title="Controversy over Cantor's theory"><span class="ilh-page"><a href="/w/index.php?title=Controversy_over_Cantor%27s_theory&action=edit&redlink=1" class="new" title="Controversy over Cantor's theory（页面不存在）">Controversy over Cantor's theory</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory" class="extiw" title="en:Controversy over Cantor's theory"><span lang="en" dir="auto">Controversy over Cantor's theory</span></a></span><span class="ilh-paren">）</span></span></span></li></ul> </div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:German_integral.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/German_integral.gif/50px-German_integral.gif" decoding="async" width="50" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/German_integral.gif/75px-German_integral.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/b/b5/German_integral.gif 2x" data-file-width="84" data-file-height="155" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#BB33DD; color:#FEFEFE">數學分支</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="Internal set theory" data-lang-code="en" data-lang-name="英语" data-foreign-title="Internal set theory"><span class="ilh-page"><a href="/w/index.php?title=Internal_set_theory&action=edit&redlink=1" class="new" title="Internal set theory（页面不存在）">Internal set theory</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Internal_set_theory" class="extiw" title="en:Internal set theory"><span lang="en" dir="auto">Internal set theory</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><span class="ilh-all" data-orig-title="Nonstandard analysis" data-lang-code="en" data-lang-name="英语" data-foreign-title="Nonstandard analysis"><span class="ilh-page"><a href="/w/index.php?title=Nonstandard_analysis&action=edit&redlink=1" class="new" title="Nonstandard analysis（页面不存在）">Nonstandard analysis</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Nonstandard_analysis" class="extiw" title="en:Nonstandard analysis"><span lang="en" dir="auto">Nonstandard analysis</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><a href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" class="mw-redirect" title="集合論">集合論</a></li> <li><span class="ilh-all" data-orig-title="Synthetic differential geometry" data-lang-code="en" data-lang-name="英语" data-foreign-title="Synthetic differential geometry"><span class="ilh-page"><a href="/w/index.php?title=Synthetic_differential_geometry&action=edit&redlink=1" class="new" title="Synthetic differential geometry（页面不存在）">Synthetic differential geometry</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Synthetic_differential_geometry" class="extiw" title="en:Synthetic differential geometry"><span lang="en" dir="auto">Synthetic differential geometry</span></a></span><span class="ilh-paren">）</span></span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#BB33DD; color:#FEFEFE">形式化</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="Cardinal number" data-lang-code="en" data-lang-name="英语" data-foreign-title="Cardinal number"><span class="ilh-page"><a href="/w/index.php?title=Cardinal_number&action=edit&redlink=1" class="new" title="Cardinal number（页面不存在）">Cardinal number</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Cardinal_number" class="extiw" title="en:Cardinal number"><span lang="en" dir="auto">Cardinal number</span></a></span><span class="ilh-paren">）</span></span></span>s</li> <li><span class="ilh-all" data-orig-title="Hyperreal number" data-lang-code="en" data-lang-name="英语" data-foreign-title="Hyperreal number"><span class="ilh-page"><a href="/w/index.php?title=Hyperreal_number&action=edit&redlink=1" class="new" title="Hyperreal number（页面不存在）">Hyperreal number</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Hyperreal_number" class="extiw" title="en:Hyperreal number"><span lang="en" dir="auto">Hyperreal number</span></a></span><span class="ilh-paren">）</span></span></span>s</li> <li><span class="ilh-all" data-orig-title="Ordinal number" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ordinal number"><span class="ilh-page"><a href="/w/index.php?title=Ordinal_number&action=edit&redlink=1" class="new" title="Ordinal number（页面不存在）">Ordinal number</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ordinal_number" class="extiw" title="en:Ordinal number"><span lang="en" dir="auto">Ordinal number</span></a></span><span class="ilh-paren">）</span></span></span>s</li> <li><a href="/wiki/%E8%B6%85%E7%8F%BE%E5%AF%A6%E6%95%B8" title="超現實數">超現實數</a></li> <li><span class="ilh-all" data-orig-title="Transfinite number" data-lang-code="en" data-lang-name="英语" data-foreign-title="Transfinite number"><span class="ilh-page"><a href="/w/index.php?title=Transfinite_number&action=edit&redlink=1" class="new" title="Transfinite number（页面不存在）">Transfinite number</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Transfinite_number" class="extiw" title="en:Transfinite number"><span lang="en" dir="auto">Transfinite number</span></a></span><span class="ilh-paren">）</span></span></span>s</li> <li><span class="ilh-all" data-orig-title="Infinitesimal" data-lang-code="en" data-lang-name="英语" data-foreign-title="Infinitesimal"><span class="ilh-page"><a href="/w/index.php?title=Infinitesimal&action=edit&redlink=1" class="new" title="Infinitesimal（页面不存在）">Infinitesimal</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Infinitesimal" class="extiw" title="en:Infinitesimal"><span lang="en" dir="auto">Infinitesimal</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><span class="ilh-all" data-orig-title="Absolute Infinite" data-lang-code="en" data-lang-name="英语" data-foreign-title="Absolute Infinite"><span class="ilh-page"><a href="/w/index.php?title=Absolute_Infinite&action=edit&redlink=1" class="new" title="Absolute Infinite（页面不存在）">Absolute Infinite</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Absolute_Infinite" class="extiw" title="en:Absolute Infinite"><span lang="en" dir="auto">Absolute Infinite</span></a></span><span class="ilh-paren">）</span></span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#BB33DD; color:#FEFEFE">數學家</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%A0%BC%E5%A5%A5%E5%B0%94%E6%A0%BC%C2%B7%E5%BA%B7%E6%89%98%E5%B0%94" title="格奥尔格·康托尔">格奧爾格·康托爾</a></li> <li><a href="/wiki/%E6%88%88%E7%89%B9%E5%BC%97%E9%87%8C%E5%BE%B7%C2%B7%E5%A8%81%E5%BB%89%C2%B7%E8%8E%B1%E5%B8%83%E5%B0%BC%E8%8C%A8" class="mw-redirect" title="戈特弗里德·威廉·莱布尼茨">戈特弗里德·威廉·萊布尼茨</a></li> <li><span class="ilh-all" data-orig-title="亞伯拉罕·羅賓遜" data-lang-code="en" data-lang-name="英语" data-foreign-title="Abraham Robinson"><span class="ilh-page"><a href="/w/index.php?title=%E4%BA%9E%E4%BC%AF%E6%8B%89%E7%BD%95%C2%B7%E7%BE%85%E8%B3%93%E9%81%9C&action=edit&redlink=1" class="new" title="亞伯拉罕·羅賓遜（页面不存在）">亞伯拉罕·羅賓遜</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Abraham_Robinson" class="extiw" title="en:Abraham Robinson"><span lang="en" dir="auto">Abraham Robinson</span></a></span><span class="ilh-paren">）</span></span></span></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">检索自“<a dir="ltr" href="https://zh.wikipedia.org/w/index.php?title=无穷&oldid=86134539">https://zh.wikipedia.org/w/index.php?title=无穷&oldid=86134539</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:%E9%A1%B5%E9%9D%A2%E5%88%86%E7%B1%BB" title="Special:页面分类">分类</a>：<ul><li><a href="/wiki/Category:%E9%9B%86%E5%90%88%E8%AE%BA" title="Category:集合论">集合论</a></li><li><a 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