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class="vector-toc-numb">二</span> <span>例</span> </div> </a> <ul id="toc-例-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="目次" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="切換目次" > <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">切換目次</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">冪集</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="前往別種語言的條目。有四七種語言可用" > <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-47" 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">四七種語言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D8%A9_%D8%A7%D9%84%D9%85%D8%AC%D9%85%D9%88%D8%B9%D8%A7%D8%AA_%D8%A7%D9%84%D8%AC%D8%B2%D8%A6%D9%8A%D8%A9" title="مجموعة المجموعات الجزئية – 阿拉伯文" lang="ar" hreflang="ar" data-title="مجموعة المجموعات الجزئية" data-language-autonym="العربية" data-language-local-name="阿拉伯文" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Conjunt_de_les_parts" title="Conjunt de les parts – 加泰蘭文" lang="ca" hreflang="ca" data-title="Conjunt de les parts" data-language-autonym="Català" data-language-local-name="加泰蘭文" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Poten%C4%8Dn%C3%AD_mno%C5%BEina" title="Potenční množina – 捷克文" lang="cs" hreflang="cs" data-title="Potenční množina" data-language-autonym="Čeština" data-language-local-name="捷克文" 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%91%D1%83%D0%BB%D0%B5%D0%B0%D0%BD" title="Булеан – 楚瓦什文" lang="cv" hreflang="cv" data-title="Булеан" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什文" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Potensm%C3%A6ngde" title="Potensmængde – 丹麥文" lang="da" hreflang="da" data-title="Potensmængde" data-language-autonym="Dansk" data-language-local-name="丹麥文" 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/Potenzmenge" title="Potenzmenge – 德文" lang="de" hreflang="de" data-title="Potenzmenge" data-language-autonym="Deutsch" data-language-local-name="德文" 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%94%CF%85%CE%BD%CE%B1%CE%BC%CE%BF%CF%83%CF%8D%CE%BD%CE%BF%CE%BB%CE%BF" title="Δυναμοσύνολο – 希臘文" lang="el" hreflang="el" data-title="Δυναμοσύνολο" data-language-autonym="Ελληνικά" data-language-local-name="希臘文" 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/Power_set" title="Power set – 英文" lang="en" hreflang="en" data-title="Power set" data-language-autonym="English" data-language-local-name="英文" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Aro_de_%C4%89iuj_subaroj" title="Aro de ĉiuj subaroj – 世界文" lang="eo" hreflang="eo" data-title="Aro de ĉiuj subaroj" data-language-autonym="Esperanto" data-language-local-name="世界文" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Conjunto_potencia" title="Conjunto potencia – 西班牙文" lang="es" hreflang="es" data-title="Conjunto potencia" data-language-autonym="Español" data-language-local-name="西班牙文" 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/Astmehulk" title="Astmehulk – 愛沙尼亞文" lang="et" hreflang="et" data-title="Astmehulk" data-language-autonym="Eesti" data-language-local-name="愛沙尼亞文" 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/Potentzia-multzo" title="Potentzia-multzo – 巴斯克文" lang="eu" hreflang="eu" data-title="Potentzia-multzo" data-language-autonym="Euskara" data-language-local-name="巴斯克文" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87_%D8%AA%D9%88%D8%A7%D9%86%DB%8C" title="مجموعه توانی – 波斯文" lang="fa" hreflang="fa" data-title="مجموعه توانی" data-language-autonym="فارسی" data-language-local-name="波斯文" 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/Potenssijoukko" title="Potenssijoukko – 芬蘭文" lang="fi" hreflang="fi" data-title="Potenssijoukko" data-language-autonym="Suomi" data-language-local-name="芬蘭文" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Alambhulk%C3%B5_hulk" title="Alambhulkõ hulk – 佛羅文" lang="vro" hreflang="vro" data-title="Alambhulkõ hulk" data-language-autonym="Võro" data-language-local-name="佛羅文" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ensemble_des_parties_d%27un_ensemble" title="Ensemble des parties d'un ensemble – 法文" lang="fr" hreflang="fr" data-title="Ensemble des parties d'un ensemble" data-language-autonym="Français" data-language-local-name="法文" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Conxunto_de_partes" title="Conxunto de partes – 加利西亞文" lang="gl" hreflang="gl" data-title="Conxunto de partes" data-language-autonym="Galego" data-language-local-name="加利西亞文" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%AA_%D7%94%D7%97%D7%96%D7%A7%D7%94" title="קבוצת החזקה – 希伯來文" lang="he" hreflang="he" data-title="קבוצת החזקה" data-language-autonym="עברית" data-language-local-name="希伯來文" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Partitivni_skup" title="Partitivni skup – 克羅埃西亞文" lang="hr" hreflang="hr" data-title="Partitivni skup" data-language-autonym="Hrvatski" data-language-local-name="克羅埃西亞文" 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/Hatv%C3%A1nyhalmaz" title="Hatványhalmaz – 匈牙利文" lang="hu" hreflang="hu" data-title="Hatványhalmaz" data-language-autonym="Magyar" data-language-local-name="匈牙利文" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Insimul_potentia" title="Insimul potentia – 國際文" lang="ia" hreflang="ia" data-title="Insimul potentia" data-language-autonym="Interlingua" data-language-local-name="國際文" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Himpunan_kuasa" title="Himpunan kuasa – 印尼文" lang="id" hreflang="id" data-title="Himpunan kuasa" data-language-autonym="Bahasa Indonesia" data-language-local-name="印尼文" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Veldismengi" title="Veldismengi – 冰島文" lang="is" hreflang="is" data-title="Veldismengi" data-language-autonym="Íslenska" data-language-local-name="冰島文" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Insieme_delle_parti" title="Insieme delle parti – 義大利文" lang="it" hreflang="it" data-title="Insieme delle parti" data-language-autonym="Italiano" data-language-local-name="義大利文" 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/%E5%86%AA%E9%9B%86%E5%90%88" title="冪集合 – 日文" lang="ja" hreflang="ja" data-title="冪集合" data-language-autonym="日本語" data-language-local-name="日文" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A9%B1%EC%A7%91%ED%95%A9" title="멱집합 – 韓文" lang="ko" hreflang="ko" data-title="멱집합" data-language-autonym="한국어" data-language-local-name="韓文" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Insemma_di_part" title="Insemma di part – 倫巴底文" lang="lmo" hreflang="lmo" data-title="Insemma di part" data-language-autonym="Lombard" data-language-local-name="倫巴底文" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D1%82%D0%B8%D1%82%D0%B8%D0%B2%D0%BD%D0%BE_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Партитивно множество – 馬其頓文" lang="mk" hreflang="mk" data-title="Партитивно множество" data-language-autonym="Македонски" data-language-local-name="馬其頓文" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Machtsverzameling" title="Machtsverzameling – 荷蘭文" lang="nl" hreflang="nl" data-title="Machtsverzameling" data-language-autonym="Nederlands" data-language-local-name="荷蘭文" 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/Potensmengd" title="Potensmengd – 耐諾斯克挪威文" lang="nn" hreflang="nn" data-title="Potensmengd" data-language-autonym="Norsk nynorsk" data-language-local-name="耐諾斯克挪威文" 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/Potensmengde" title="Potensmengde – 巴克摩挪威文" lang="nb" hreflang="nb" data-title="Potensmengde" data-language-autonym="Norsk bokmål" data-language-local-name="巴克摩挪威文" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Zbi%C3%B3r_pot%C4%99gowy" title="Zbiór potęgowy – 波蘭文" lang="pl" hreflang="pl" data-title="Zbiór potęgowy" data-language-autonym="Polski" data-language-local-name="波蘭文" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Ansem_potensa" title="Ansem potensa – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Ansem potensa" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Conjunto_de_partes" title="Conjunto de partes – 葡萄牙文" lang="pt" hreflang="pt" data-title="Conjunto de partes" data-language-autonym="Português" data-language-local-name="葡萄牙文" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%BE_%D0%B2%D1%81%D0%B5%D1%85_%D0%BF%D0%BE%D0%B4%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2" title="Множество всех подмножеств – 俄文" lang="ru" hreflang="ru" data-title="Множество всех подмножеств" data-language-autonym="Русский" data-language-local-name="俄文" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Power_set" title="Power set – Simple English" lang="en-simple" hreflang="en-simple" data-title="Power set" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Poten%C4%8Dn%C3%A1_mno%C5%BEina" title="Potenčná množina – 斯洛伐克文" lang="sk" hreflang="sk" data-title="Potenčná množina" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克文" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Bashk%C3%ABsia_partitive" title="Bashkësia partitive – 阿爾巴尼亞文" lang="sq" hreflang="sq" data-title="Bashkësia partitive" data-language-autonym="Shqip" data-language-local-name="阿爾巴尼亞文" 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%9F%D0%B0%D1%80%D1%82%D0%B8%D1%82%D0%B8%D0%B2%D0%BD%D0%B8_%D1%81%D0%BA%D1%83%D0%BF" title="Партитивни скуп – 塞爾維亞文" lang="sr" hreflang="sr" data-title="Партитивни скуп" data-language-autonym="Српски / srpski" data-language-local-name="塞爾維亞文" 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/Potensm%C3%A4ngd" title="Potensmängd – 瑞典文" lang="sv" hreflang="sv" data-title="Potensmängd" data-language-autonym="Svenska" data-language-local-name="瑞典文" 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%85%E0%AE%9F%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%81_%E0%AE%95%E0%AE%A3%E0%AE%AE%E0%AF%8D" title="அடுக்கு கணம் – 坦米爾文" lang="ta" hreflang="ta" data-title="அடுக்கு கணம்" data-language-autonym="தமிழ்" data-language-local-name="坦米爾文" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%8B%E0%B8%95%E0%B8%81%E0%B8%B3%E0%B8%A5%E0%B8%B1%E0%B8%87" title="เซตกำลัง – 泰文" lang="th" hreflang="th" data-title="เซตกำลัง" data-language-autonym="ไทย" data-language-local-name="泰文" 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/Kapangyarihang_pangkat" title="Kapangyarihang pangkat – 塔加路族文" lang="tl" hreflang="tl" data-title="Kapangyarihang pangkat" data-language-autonym="Tagalog" data-language-local-name="塔加路族文" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D1%83%D0%BB%D0%B5%D0%B0%D0%BD" title="Булеан – 烏克蘭文" lang="uk" hreflang="uk" data-title="Булеан" data-language-autonym="Українська" data-language-local-name="烏克蘭文" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%E1%BA%ADp_l%C5%A9y_th%E1%BB%ABa" title="Tập lũy thừa – 越南文" lang="vi" hreflang="vi" data-title="Tập lũy thừa" data-language-autonym="Tiếng Việt" data-language-local-name="越南文" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%86%AA%E9%9B%86" title="冪集 – 中文" lang="zh" hreflang="zh" data-title="冪集" data-language-autonym="中文" data-language-local-name="中文" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%86%AA%E9%9B%86" title="冪集 – 粵語" lang="yue" hreflang="yue" data-title="冪集" data-language-autonym="粵語" data-language-local-name="粵語" 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/Q205170#sitelinks-wikipedia" title="修跨語鏈" class="wbc-editpage">纂鏈</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="名集"> <div 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class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 付梓 </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=%E7%89%B9%E6%AE%8A:DownloadAsPdf&page=%E5%86%AA%E9%9B%86&action=show-download-screen"><span>存為PDF檔</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="備印墨，整版貌[p]" accesskey="p"><span>付梓</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"> 諸策 </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:Power_set" hreflang="en"><span>維基共享</span></a></li><li id="t-wikibase" class="wb-otherproject-link 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data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">外觀</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至側邊欄</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隱藏</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-indicator-fr-review-status" class="mw-indicator"><indicator name="fr-review-status" class="mw-fr-review-status-indicator" id="mw-fr-revision-toggle"><span class="cdx-fr-css-icon-review--status--unchecked"></span><b><a href="/wiki/%E8%AA%AA%E6%98%8E:%E6%A0%A1%E5%B0%8D" title="說明:校對">今本</a></b>（此為底本，未經審校）</indicator></div> </div> <div id="siteSub" class="noprint">文出維基大典</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div id="mw-fr-revision-details" class="mw-fr-revision-details-dialog" style="display:none;"><div tabindex="0"></div><div class="cdx-dialog cdx-dialog--horizontal-actions"><header class="cdx-dialog__header cdx-dialog__header--default"><div class="cdx-dialog__header__title-group"><h2 class="cdx-dialog__header__title">頁面版本狀態</h2><p class="cdx-dialog__header__subtitle">該頁面尚未檢查</p></div><button class="cdx-button cdx-button--action-default cdx-button--weight-quiet
							cdx-button--size-medium cdx-button--icon-only cdx-dialog__header__close-button" aria-label="關閉" onclick="document.getElementById("mw-fr-revision-details").style.display = "none";" type="submit"><span class="cdx-icon cdx-icon--medium
							cdx-fr-css-icon--close"></span></button></header><div class="cdx-dialog__body">此為底本，未經<a href="/wiki/%E8%AA%AA%E6%98%8E:%E6%A0%A1%E5%B0%8D" title="說明:校對">審校</a>。</div></div><div tabindex="0"></div></div><div class="mw-content-ltr mw-parser-output" lang="lzh" dir="ltr"><div style="border:1px solid #A3B1BF; padding:0.5em 2em; width:60%; float:left;"> 註︰蓋當今數學之事，誠難僅以文述，而無符號，故凡數學之文，咸有漢字、拉丁字相易之事，以合文言、數學，則無論文理之人，皆可明之也。</div> <div style="clear:left;"></div> <p><b>冪集</b>，諸<a href="/wiki/%E5%AD%90%E9%9B%86" title="子集">子集</a>之合也。 </p> <div class="mw-heading mw-heading2"><h2 id="定義"><span id=".E5.AE.9A.E7.BE.A9"></span>定義</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%86%AA%E9%9B%86&action=edit&section=1" title="所纂章名：定義"><span>纂</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>甲（<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/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>）之子集，俱聚而成<a href="/wiki/%E9%9B%86" title="集">集</a>而無一漏省，曰甲之冪集（記曰「<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 P(A)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(A)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f264d19e21604793c6dc54f8044df454db82744" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.298ex; height:2.843ex;" alt="{\displaystyle P(A)}"></span>，即<i>冪</i>（<i>甲</i>）」）。舉甲集有水、火兩<a href="/wiki/%E5%85%83%E7%B4%A0" class="mw-redirect" title="元素">元</a>為例，甲之冪集為「{}，{水}，{火}，{水,火}」。 </p><p>冪集公理曰︰「若有集，則其冪集亦存。」 </p> <div class="mw-heading mw-heading2"><h2 id="例"><span id=".E4.BE.8B"></span>例</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%86%AA%E9%9B%86&action=edit&section=2" title="所纂章名：例"><span>纂</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>尋歲寒三友，或無所得，或見松，或見竹，或見梅，或見「松、竹」，或見「松、梅」，或見「竹、梅」，或咸得之。此八見，歲寒三友之冪集也。（「<i>P</i>({1,2,3})={ Φ, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} }」）</li> <li><a href="/wiki/%E7%A9%BA%E9%9B%86" title="空集">空集</a>者，凡冪集必有之。（「Φ ∈ <i>P</i>(<i>A</i>)」）</li> <li>空集之冪集，以空集為物之集也。（「<i>P</i>(Φ) = { Φ }」）</li></ul> <div class="NavFrame" style="clear:both"> <div class="NavHead"><a href="/wiki/%E9%9B%86%E8%AB%96" title="集論">集論</a></div> <div class="NavContent"> <p><a href="/wiki/%E9%9B%86" title="集">元素</a>｜ <a href="/wiki/%E9%9B%86" title="集">集</a>｜ <a href="/wiki/%E6%97%8F_(%E6%95%B8%E5%AD%B8)" title="族 (數學)">族</a>｜ <a href="/wiki/%E5%AD%90%E9%9B%86" title="子集">子集</a>｜ <a href="/wiki/%E4%BA%A4%E9%9B%86" title="交集">交集</a>｜ <a href="/wiki/%E4%BD%B5%E9%9B%86" title="併集">併集</a>｜ <a href="/wiki/%E8%A3%9C%E9%9B%86" title="補集">補集</a>｜ <a class="mw-selflink selflink">冪集</a>｜ <a href="/wiki/%E6%9C%89%E5%BA%8F%E5%B0%8D" title="有序對">有序對</a>｜ <a href="/wiki/%E7%9B%B4%E7%A9%8D" title="直積">直積</a>｜ <a href="/wiki/%E9%97%9C%E4%BF%82_(%E6%95%B8%E5%AD%B8)" title="關係 (數學)">關係</a>｜ <a href="/wiki/%E6%98%A0%E5%B0%84" title="映射">映射</a>｜ <a href="/wiki/%E7%AD%89%E5%83%B9" title="等價">等價</a>｜ <a href="/wiki/%E5%81%8F%E5%BA%8F" title="偏序">偏序</a> </p> </div> <div class="NavEnd"> </div> </div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">取自「<a dir="ltr" href="https://zh-classical.wikipedia.org/wiki/冪集">https://zh-classical.wikipedia.org/wiki/冪集</a>」</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%E7%89%B9%E6%AE%8A:%E9%A1%9E" title="特殊:類">二類</a>：<ul><li><a href="/wiki/%E5%88%86%E9%A1%9E:%E9%9B%86%E5%90%88" title="分類:集合">集合</a></li><li><a href="/wiki/%E5%88%86%E9%A1%9E:%E6%95%B8%E5%AD%B8" title="分類:數學">數學</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-copyright">凡我維基之文，悉為<a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">共享創意授權</a>。翻印增刪，皆須引據，並同道為之。然條款繁多，不一而足。請閱<a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">全文</a>，以得其詳。<br /></li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">隱私通例</a></li> <li id="footer-places-about"><a href="/wiki/%E6%96%87%E8%A8%80%E7%B6%AD%E5%9F%BA%E5%A4%A7%E5%85%B8">大典自序</a></li> <li id="footer-places-disclaimers"><a href="https://en.wikipedia.org/wiki/Wikipedia:General_disclaimer">免責告示</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">行為準則</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">司空津逮</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/zh-classical.wikipedia.org">彙統</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">鑑識聲明</a></li> <li id="footer-places-mobileview"><a href="//zh-classical.m.wikipedia.org/w/index.php?title=%E5%86%AA%E9%9B%86&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">掌中書卷</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5ccf8d5c58-n4nk8","wgBackendResponseTime":189,"wgPageParseReport":{"limitreport":{"cputime":"0.015","walltime":"0.051","ppvisitednodes":{"value":42,"limit":1000000},"postexpandincludesize":{"value":1104,"limit":2097152},"templateargumentsize":{"value":232,"limit":2097152},"expansiondepth":{"value":5,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":72,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 10.786 1 -total"," 64.80% 6.989 1 模板:集論"," 32.74% 3.531 1 模板:Navigationsleiste"," 32.45% 3.500 1 模板:當代數學"]},"cachereport":{"origin":"mw-web.codfw.main-694cf4987f-8gm9h","timestamp":"20241125230942","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"\u51aa\u96c6","url":"https:\/\/zh-classical.wikipedia.org\/wiki\/%E5%86%AA%E9%9B%86","sameAs":"http:\/\/www.wikidata.org\/entity\/Q205170","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q205170","author":{"@type":"Organization","name":"\u7dad\u57fa\u5a92\u9ad4\u5c08\u6848\u8ca2\u737b\u8005"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2007-10-08T02:42:22Z"}</script> </body> </html>