Difference between revisions of "Language/Multiple-languages/Vocabulary/Mathematical-Logic"
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{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 科目 | |||
! cmn-Hans-CN: | ! cmn-Latn.Pinyin-CN: kēmù | ||
! cmn-Latn.Pinyin-CN: | ! deu-Latn-DE: Fach [n] | ||
! deu-Latn-DE: | ! eng-Latn-US: subject | ||
! fra-Latn-FR: | ! fra-Latn-FR: matière [f] | ||
! jpn-Jpan-JP: | ! jpn-Jpan-JP: 科目 | ||
! jpn-Hrkt-JP: | ! jpn-Hrkt-JP: か↑もく | ||
! pes-Aran-IR: | ! pes-Aran-IR: رِشته | ||
! rus-Cyrl-RU: | ! rus-Cyrl-RU: предме́т | ||
|- | |- | ||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| 集合论 | |||
| 集合论 | | jíhé lùn | ||
| jíhé lùn | | Mengenlehre [f] | ||
| Mengenlehre [f] | | | set theory | ||
| théorie [f] des ensembles | | théorie [f] des ensembles [m pl] | ||
| 集合論 | | 集合論 | ||
| しゅ↑うご↓うろん | | しゅ↑うご↓うろん | ||
| | |||
| тео́рия мно́жеств | | тео́рия мно́жеств | ||
|- | |- | ||
| 公理化集合论 | |||
| 公理化集合论 | | gǒnglǐhuà jíhélùn | ||
| gǒnglǐhuà jíhélùn | | axiomatische Mengenlehre | ||
| axiomatische Mengenlehre | | | axiomatic set theory | ||
| théorie [f] axiomatique des ensembles || | | théorie [f] axiomatique des ensembles [m pl] | ||
| | | 公理的集合論 | ||
| | | こ↑うりてき↓しゅ↑うご↓うろん | ||
| | | | ||
| | | аксиомати́ческая тео́рия мно́жеств | ||
|- | |||
| 证明论 | |||
| zhèngmíng lùn | |||
| Beweistheorie [f] | |||
| proof theory | |||
| théorie [f] de la démonstration, théorie [f] de la preuve | |||
| 証明論 | |||
| しょ↑うめ↓いろん | |||
| | |||
| тео́рия доказа́тельств | |||
|- | |- | ||
| | | 模型论 | ||
| móxíng lùn | |||
| | | Modelltheorie [f] | ||
| | | model theory | ||
| théorie [f] | | théorie [f] des modèles [m pl] | ||
| | | モデル理論 | ||
| | | モ↑デルり↓ろん | ||
| | |||
| тео́рия | | тео́рия моде́лей | ||
|- | |- | ||
| | | 可计算性理论 | ||
| | | kějìsuànxìng lǐlùn | ||
| | | Berechenbarkeitstheorie [f], Rekursionstheorie [f] | ||
| computability theory, recursion theory | |||
| théorie [f] | | théorie [f] de la calculabilité | ||
| | | 計算可能性理論 | ||
| | | け↑いさんかのうせいり↓ろん | ||
| | |||
| тео́рия | | тео́рия вычисли́мости | ||
|- | |- | ||
| | | 类型论 | ||
| lèixíng lùn | |||
| | | Typentheorie [f] | ||
| | | type theory | ||
| théorie [f] | | théorie [f] des types [m pl] | ||
| | | 型理論 | ||
| | | か↑たり↓ろん | ||
| | |||
| | | тео́рией ти́пов | ||
|- | |- | ||
| | | 代数逻辑 | ||
| | | dàishù luóji | ||
| | | algebraische Logik | ||
| | | algebraic logic | ||
| | | logique [f] algébrique | ||
| | |||
| | |||
| | |||
| | | алгебраи́ческая ло́гика | ||
|- | |- | ||
| | | 逻辑代数,布尔代数 | ||
| | | luóji dàishù, Bù'ěr dàishù | ||
| | | boolesche Algebra, boolescher Verband | ||
| | | Boolean algebra | ||
| | | algèbre [f] de Boole, algèbre booléenne | ||
| | | ブール代数,ブール束 | ||
| | | ブ↑ールだ↓いすう,ブ↑ールそく | ||
| | |||
| а́лгебра ло́гики, а́лгебра выска́зываний | |||
|- | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|} | |||
{| class="wikitable sortable" | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | |||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | |||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | |||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | |||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | |||
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیشنیاز | |||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
|- | |||
| 函数空间 || | |||
| hánshù kōngjiān || | |||
| Funktionenraum [m] || | |||
| function space || set; function | |||
| espace fonctionnel || | |||
| || | |||
| 関数空間 || | |||
| か↑んすうく↓うかん || | |||
| функциона́льное простра́нство || | |||
|- | |||
| 数学对象 || | |||
| shùxué duìxiàng || | |||
| mathematisches Objekt || | |||
| mathematical object || | |||
| objet [m] mathématique || | |||
| || | | || | ||
| 数学的対象 || | |||
| す↑うがくてきた↓いしょう || | |||
| математи́ческий объе́кт || | |||
|- | |- | ||
| || | | || | ||
Line 121: | Line 165: | ||
|} | |} | ||
== Set Theory == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
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| || | | || | ||
|- | |- | ||
| 参数 || | | 参数 || | ||
| cān shù || | | cān shù || | ||
| Argument [m] || | | Argument [m] || | ||
| argument || function | |||
| argument [m] || | | argument [m] || | ||
| 引数 || | | 引数 || | ||
| ひ↑きす↓う || | | ひ↑きす↓う || | ||
| || | | || | ||
| | | аргуме́нт || | ||
|- | |- | ||
| 双射 || | | 双射 || | ||
| shuāng shè || | | shuāng shè || | ||
| Bijektion [f], bijektive Funktion || | | Bijektion [f], bijektive Funktion || | ||
| bijection, bijective function, invertible function || function; set | |||
| bijection [f] || | | bijection [f] || | ||
| 全単射,双射 || | | 全単射,双射 || | ||
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| бие́кция || | | бие́кция || | ||
|- | |- | ||
| 二元运算 || | | 二元运算 || | ||
| èryuán yùnsuàn || | | èryuán yùnsuàn || | ||
| zweistellige Verknüpfung, binäre Verknüpfung || | | zweistellige Verknüpfung, binäre Verknüpfung || | ||
| binary operation, dyadic operation || operation | |||
| opération [f] binaire || | | opération [f] binaire || | ||
| 二項演算 || | | 二項演算 || | ||
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| бина́рная опера́ция, двуме́стная опера́ция || | | бина́рная опера́ция, двуме́стная опера́ция || | ||
|- | |- | ||
| 势,浓度 || | | 势,浓度 || | ||
| shì, nóng dù || | | shì, nóng dù || | ||
| Mächtigkeit [f], Kardinalität [f] || | | Mächtigkeit [f], Kardinalität [f] || | ||
| cardinality || set | |||
| cardinalité [f] || | | cardinalité [f] || | ||
| 濃度,カーディナリティ || | | 濃度,カーディナリティ || | ||
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| мо́щность || | | мо́щность || | ||
|- | |- | ||
| 基数 || | | 基数 || | ||
| jī shù || | | jī shù || | ||
| Kardinalzahl [f] || | | Kardinalzahl [f] || | ||
| nombre cardinal | | cardinal number, cardinal || cardinality | ||
| nombre cardinal, cardinal [m] || | |||
| 基数 || | | 基数 || | ||
| き↑す↓う || | | き↑す↓う || | ||
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| кардина́льное число́ || | | кардина́льное число́ || | ||
|- | |- | ||
| 笛卡尔积 || | | 笛卡尔积 || | ||
| Díkǎ'ěr jī || | | Díkǎ'ěr jī || | ||
| kartesisches Produkt, Mengenprodukt [n] || | | kartesisches Produkt, Mengenprodukt [n] || | ||
| produit | | Cartesian product || ordered pair | ||
| produit cartésien || | |||
| 直積,デカルト積 || | | 直積,デカルト積 || | ||
| ちょ↑くせ↓き,デ↑カルトせ↓き || | | ちょ↑くせ↓き,デ↑カルトせ↓き || | ||
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| прямо́е произведе́ние, дека́ртово произведе́ние || | | прямо́е произведе́ние, дека́ртово произведе́ние || | ||
|- | |- | ||
| 选择函数 || | | 选择函数 || | ||
| xuǎnzé hánshù || | | xuǎnzé hánshù || | ||
| Auswahlfunktion [f] || | | Auswahlfunktion [f] || | ||
| fonction [f] de choix || | | choice function || function; empty set; direct product <algebra> | ||
| fonction [f] de choix [m] || | |||
| 選択関数 || | | 選択関数 || | ||
| せ↑んたくか↓んすう || | | せ↑んたくか↓んすう || | ||
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| фу́нкция вы́бора || | | фу́нкция вы́бора || | ||
|- | |- | ||
| 类 || | | 类 || | ||
| lèi || | | lèi || | ||
| Klasse [f] || | | Klasse [f] || | ||
| class || set | |||
| classe [f] || | | classe [f] || | ||
| クラス,類 || | | クラス,類 || | ||
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| класс || | | класс || | ||
|- | |- | ||
| 到达域,陪域,上域,终域 || | | 到达域,陪域,上域,终域 || | ||
| dàodá yù, péi yù, shàng yù, zhōng yù || | | dàodá yù, péi yù, shàng yù, zhōng yù || | ||
| Zielmenge [f], Wertevorrat [m] || | | Zielmenge [f], Wertevorrat [m] || | ||
| codomain, set of destination || function | |||
| ensemble [m] d'arrivée [f] || | | ensemble [m] d'arrivée [f] || | ||
| 終域 || | | 終域 || | ||
| | | し↑ゅうい↓き || | ||
| || | |||
| || | | || | ||
|- | |- | ||
| 连续统 || | | 连续统 || | ||
| liánxù tǒng || | | liánxù tǒng || | ||
| Kontinuum [m] || | | Kontinuum [m] || | ||
| continuum || cardinal number | |||
| continu [m] || | | continu [m] || | ||
| 連続体 || | | 連続体 || | ||
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| конти́нуум || | | конти́нуум || | ||
|- | |- | ||
| 定义域 || | | 定义域 || | ||
| dìngyì yù || | | dìngyì yù || | ||
| Definitionsmenge [f], Definitionsbereich [m] || | | Definitionsmenge [f], Definitionsbereich [m] || | ||
| ensemble [m] de définition || | | domain, set of departure || function | ||
| ensemble [m] de définition [f] || | |||
| 定義域 || | | 定義域 || | ||
| て↑いぎ↓いき || | | て↑いぎ↓いき || | ||
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| о́бласть определе́ния || | | о́бласть определе́ния || | ||
|- | |- | ||
| 元素 || | | 元素 || | ||
| yuánsù || | | yuánsù || | ||
| Element [n] || | | Element [n] || | ||
| element || mathematical object | |||
| élément [m] || | | élément [m] || | ||
| 元 || | | 元 || | ||
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| элеме́нт || | | элеме́нт || | ||
|- | |- | ||
| 列举法 || | | 列举法 || | ||
| lièjǔ fǎ || | | lièjǔ fǎ || | ||
| Aufzählung [f] || | | Aufzählung [f] || | ||
| enumeration || set | |||
| énumération [f] || | | énumération [f] || | ||
| 数え上げ || | | 数え上げ || | ||
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| перечисле́ние || | | перечисле́ние || | ||
|- | |- | ||
| 相等 || | | 相等 || | ||
| xiāng děng || | | xiāng děng || | ||
| Gleichheit [f] || | | Gleichheit [f] || | ||
| equality || | |||
| égalité [f] || | | égalité [f] || | ||
| | | 相等 || | ||
| | | そ↑うとう || | ||
| تَساوی || | | تَساوی || | ||
| | | ра́венство || | ||
|- | |- | ||
| 表达式,表示式,运算式 || | | 表达式,表示式,运算式 || | ||
| biǎodá shì, biǎoshì shì, yùnsuàn shì || | | biǎodá shì, biǎoshì shì, yùnsuàn shì || | ||
| Ausdruck [m] || | | Ausdruck [m] || | ||
| expression || digit; symbol | |||
| expression [f] || | | expression [f] || | ||
| 数式 || | |||
| す↑うしき || | |||
| || | | || | ||
| | | выраже́ние || | ||
|- | |- | ||
| 外延性 || | |||
| wàiyán xìng || | |||
| Extensionalität [f] || | |||
| extensionality, extensional equality || mathematical object | | extensionality, extensional equality || mathematical object | ||
| extensionnalité [f] || | |||
| 外延性 || | |||
| が↑いえんせい || | |||
| || | | || | ||
| экстенсиона́льность [ж] || | |||
|- | |||
| 单位元 || | |||
| dānwèi yuán || | |||
| neutrales Element || | |||
| identity element, neutral element || binary operation; set | |||
| élément [m] neutre, élément [m] identité || | |||
| 単位元,中立元 || | |||
| た↑んいげ↓ん,ちゅ↑うりつげ↓ん || | |||
| || | | || | ||
| нейтра́льный элеме́нт || | |||
|- | |||
| 恒等函数 || | |||
| héngděng hánshù || | |||
| identische Abbildung || | |||
| identity function, identity relation, identity map, identity transformation || argument | |||
| application [f] identité, fonction [f] identité || | |||
| 恒等写像 || | |||
| こ↑うとうしゃ↓ぞう || | |||
| || | | || | ||
| тожде́ственное отображе́ние || | |||
|- | |||
| 像 || | |||
| xiàng || | |||
| Bild [n], Bildbereich [m], Bildmenge [f] || | |||
| image || function | |||
| image [f] || | |||
| 像 || | |||
| ぞ↓う || | |||
| || | | || | ||
| о́браз || | |||
|- | |||
| 族 || | |||
| zú || | |||
| Familie [f] || | |||
| indexed family, family || set | |||
| famille || | |||
| 族 || | |||
| ぞ↑く || | |||
| || | | || | ||
| семе́йство, индекси́рованное семе́йство || | |||
|- | |||
| 不等 || | |||
| bù děng || | |||
| Ungleichheit [f] || | |||
| inequality || equality | |||
| inégalité [f] || | |||
| 不等 || | |||
| ふ↑とう || | |||
| || | | || | ||
| нера́венство || | |||
|- | |||
| 单射 || | |||
| dān shè || | |||
| injektive Funktion || | |||
| injection, injective function, one-to-one function || function; injectivity | |||
| injection [f] || | |||
| 単射 || | |||
| た↑んしゃ || | |||
| || | | || | ||
| инъе́кция, инъекти́вное отображе́ние || | |||
|- | |||
| 原像 || | |||
| yuán xiàng || | |||
| Urbild [n] || | |||
| inverse image, preimage || codomain; subset | |||
| image [f] réciproque, préimage [f] || | |||
| 逆像,原像 || | |||
| ぎゃ↑くぞう,げ↑んぞう || | |||
| || | | || | ||
| обра́тный о́браз, проо́браз || | |||
|- | |- | ||
| | | 映射 || | ||
| | | yìngshè || | ||
| | | Abbildung [f] || | ||
| | | mapping || function | ||
| | | application [f] || | ||
| 写像 || | |||
| しゃ↑ぞう || | |||
| || | | || | ||
| отображе́ние || | |||
|- | |||
| 运算数,运算元 || | |||
| yùnsuàn shù, yùnsuàn yuán || | |||
| Operand [m] || | |||
| operand || operation | |||
| opérande [m] || | |||
| 被演算子 || | |||
| ひ↑えんざ↓んし || | |||
| || | | || | ||
| опера́нд || | |||
|- | |||
| 运算 || | |||
| yùnsuàn || | |||
| Verknüpfung [f] || | |||
| operation || | |||
| opération [f] || | |||
| 演算 || | |||
| え↑んざん || | |||
| || | | || | ||
| oпера́ция || | |||
|- | |||
| 序数 || | |||
| xù shù || | |||
| Ordinalzahl [f] || | |||
| ordinal number || enumeration; ordinal numeral <linguistics> | |||
| nombre ordinal || | |||
| 順序数 || | |||
| じゅ↑んじょ↓すう || | |||
| || | | || | ||
| поря́дковым число́м, ордина́лом || | |||
|- | |- | ||
| | | 值域 || | ||
| zhí yù || | |||
| Bild [n] (Funktion), Bildbereich [m] (Funktion), Bildmenge [f] (Funktion) || | |||
| range || image | |||
| image [f] (application) || | |||
| 値域 || | |||
| ち↓いき || | |||
| || | | || | ||
| о́бласть значе́ний фу́нкции, мно́жество значе́ний фу́нкции || | |||
|- | |||
| 关系 || | |||
| guānxi || | |||
| Relation [f] || | |||
| relation || set | |||
| relation [f] || | |||
| 関係 || | |||
| かんけい || | |||
| || | | || | ||
| отноше́ние || | |||
|- | |||
| 罗素悖论 || | |||
| Luósù bèilùn || | |||
| Russellsche Antinomie || | |||
| Russell's paradox, Russell's antinomy || set | |||
| paradoxe [m] de Russell, antinomie [f] de Russell || | |||
| ラッセルのパラドックス || | |||
| ラ↓ッセルのパ↑ラド↓ックス || | |||
| || | | || | ||
| парадо́кс Ра́ссела, антино́мия Ра́ссела || | |||
|- | |||
| 集合,集 || | |||
| jíhé, jí || | |||
| Menge [f] || | |||
| set || element | |||
| ensemble [m] || | |||
| 集合 || | |||
| しゅ↑うごう || | |||
| || | | || | ||
| мно́жество || | |||
|- | |||
| 满射 || | |||
| mǎn shè || | |||
| surjektive Funktion || | |||
| surjection, surjective function, onto function || function | |||
| surjection [f], application surjective || | |||
| 全射 || | |||
| ぜ↑んしゃ || | |||
| || | | || | ||
| сюръе́кция, сюръекти́вное отображе́ние || | |||
|- | |||
| 对称差 || | |||
| duìchèn chā || | |||
| symmetrische Differenz || | |||
| symmetric difference, disjunctive union || intersection | |||
| différence [f] symétrique || | |||
| 対称差 || | |||
| た↑いしょうさ || | |||
| || | | || | ||
| симметри́ческая ра́зность || | |||
|- | |||
| 多元组 || | |||
| duōyuán zǔ || | |||
| Tupel [n] || | |||
| tuple || element; sequence <number theory> | |||
| uplet [m] || | |||
| 順序組,組 || | |||
| じゅ↑んじょぐみ,く↑み || | |||
| || | | || | ||
| корте́ж || | |||
|- | |||
| 全集 || | |||
| quán jí || | |||
| Universalmenge [f], Allmenge [f], Grundmenge [f] || | |||
| universal set || universe | |||
| ensemble référentiel || | |||
| 全体集合,普遍集合 || | |||
| ぜ↑んたいしゅ↓うごう,ふ↑へんしゅ↓うごう || | |||
| || | | || | ||
| универса́льное мно́жество || | |||
|- | |- | ||
| | | 全类 || | ||
| | | quán lèi || | ||
| | | Universum [n] || | ||
| | | universe || class | ||
| | | univers [m] || | ||
| 宇宙 || | |||
| う↓ちゅう || | |||
| || | | || | ||
| универса́льный класс || | |||
|- | |||
| 基本元素 || | |||
| jīběn yuánsù || | |||
| Urelement [n] || | |||
| urelement || set | |||
| ur-element [m] || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| урэлеме́нт || | |||
|- | |- | ||
| | | 范恩图,维恩图,韦恩图,文氏图 || | ||
| | | Fàn'ēn tú, Wéi'ēn tú, Wéi'ēn tú, Wénshì tú || | ||
| Venn-Diagramm [n] || | |||
| | | Venn diagram || set | ||
| | | diagramme [m] de Venn || | ||
| | | ベン図,ヴェン図 || | ||
| | | ベ↓ンず、ヴェ↓ンず || | ||
| | |||
| || | | || | ||
| диагра́мма Ве́нна || | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
Line 353: | Line 575: | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|} | |||
{| class="wikitable sortable" | |||
|+ property of binary operation | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | |||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | |||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | |||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | |||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | |||
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیشنیاز | |||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | |||
| property of binary operation || | |||
| || | | || | ||
| || | | || | ||
Line 364: | Line 600: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | |||
| || | |||
|- | |||
| 反交换律 || | |||
| fǎnjiāohuàn lǜ || | |||
| Antikommutativgesetz [n], Antikommutativität [f] || | |||
| anticommutative property, anticommutativity || operation | |||
| || | | || | ||
| || | | || | ||
Line 384: | Line 620: | ||
| || | | || | ||
|- | |- | ||
| | | 结合律 || | ||
| jiéhé lǜ || | |||
| Assoziativgesetz [n], Assoziativität [f] || | |||
| associative property, associativity || operation | |||
| || | |||
| || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| 交换律 || | |||
| jiāohuàn lǜ || | |||
| Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f] || | |||
| commutative property, commutativity || operation | |||
| || | | || | ||
| || | | || | ||
Line 394: | Line 640: | ||
| || | | || | ||
|- | |- | ||
| | | 分配律 || | ||
| fēnpèi lǜ || | |||
| Distributivgesetz [n], Distributivität [f] || | |||
| distributive property, distributivity || operation | |||
| || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 423: | Line 659: | ||
| || | | || | ||
| || | | || | ||
|} | |||
{| class="wikitable sortable" | |||
|+ operation on set | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | |||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | |||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | |||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | |||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | |||
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیشنیاز | |||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| operation on set || | |||
| || | | || | ||
| || | | || | ||
Line 434: | Line 683: | ||
| || | | || | ||
|- | |- | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
Line 444: | Line 693: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| absolute complement || complement; subset | |||
| || | | || | ||
| || | | || | ||
Line 454: | Line 703: | ||
| || | | || | ||
|- | |- | ||
| | | 补集 || | ||
| | | bǔ jí || | ||
| | | Komplement [n] || | ||
| complement, set difference || set | |||
| | | complémentaire [m] || | ||
| | | 差集合 || | ||
| | | さ↑しゅ↓うごう || | ||
| | |||
| || | | || | ||
| ра́зность мно́жеств || | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| intersection || set | |||
| || | | || | ||
| || | | || | ||
Line 474: | Line 723: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| power set, powerset || subset; empty set | |||
| || | | || | ||
| || | | || | ||
Line 484: | Line 733: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| relative complement || complement; subset | |||
| || | | || | ||
| || | | || | ||
Line 494: | Line 743: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| union || set | |||
| || | | || | ||
| || | | || | ||
Line 504: | Line 753: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 523: | Line 762: | ||
| || | | || | ||
| || | | || | ||
|} | |||
{| class="wikitable sortable" | |||
|+ system of set theory | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | |||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | |||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | |||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | |||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | |||
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیشنیاز | |||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| system of set theory || | |||
| || | | || | ||
| || | | || | ||
Line 534: | Line 786: | ||
| || | | || | ||
|- | |- | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
Line 544: | Line 796: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Zermelo–Fraenkel set theory || axiomatic system | |||
| || | | || | ||
| || | | || | ||
Line 566: | Line 818: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ | |+ type of set | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 577: | Line 829: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| type of set || | |||
| || | | || | ||
| || | | || | ||
Line 597: | Line 849: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | |||
| countable set || subset; cardinality | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | empty set || set | ||
| || | | || | ||
| || | | || | ||
Line 627: | Line 869: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | |||
| finite set || set | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
| || | | || | ||
| || | |||
| fuzzy set, uncertain set || set | |||
| || | | || | ||
| || | | || | ||
Line 646: | Line 888: | ||
| || | | || | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| infinite set || set | |||
| || | | || | ||
| || | | || | ||
Line 673: | Line 902: | ||
| || | | || | ||
| || | | || | ||
| | | proper subset || subset | ||
| || | | || | ||
| || | | || | ||
Line 680: | Line 909: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| singleton. unit set || set | |||
| || | | || | ||
| || | | || | ||
Line 690: | Line 919: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| | | || | ||
| || | |||
| subset || set | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| superset || set | |||
| || | | || | ||
| || | | || | ||
Line 710: | Line 939: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| transitive set || subset; urelement | |||
| || | | || | ||
| || | | || | ||
Line 720: | Line 949: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| universal set || mathematical object | |||
| || | | || | ||
| || | | || | ||
Line 730: | Line 959: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| unordered pair, pair set || set | |||
| || | | || | ||
| || | | || | ||
Line 743: | Line 972: | ||
| || | | || | ||
| || | | || | ||
| well-founded set || transitive closure | |||
| || | | || | ||
| || | | || | ||
Line 748: | Line 978: | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
|} | | || | ||
| || | |||
{| class="wikitable sortable" | | well-ordered set || well-order; total order; non-empty set; least element | ||
|+ | | || | ||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|} | |||
{| class="wikitable sortable" | |||
|+ binary relation | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 763: | Line 1,012: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| | | 二元关系 || | ||
| èryuán guānxi || | |||
| binäre Relation || | |||
| binary relation || relation | |||
| relation [f] binaire || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
|- | |||
| || | | || | ||
| || | | || | ||
Line 786: | Line 1,035: | ||
| || | | || | ||
| || | | || | ||
| | | connected relation, total relation || binary relation | ||
| || | | || | ||
| || | | || | ||
Line 796: | Line 1,045: | ||
| || | | || | ||
| || | | || | ||
| | | converse relation || binary relation | ||
| || | | || | ||
| || | | || | ||
Line 803: | Line 1,052: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| equivalence relation || reflexive relation; symmetric relation; transitive relation | |||
| || | | || | ||
| || | | || | ||
Line 816: | Line 1,065: | ||
| || | | || | ||
| || | | || | ||
| finitary relation || Cartesian product | |||
| || | | || | ||
| || | | || | ||
Line 821: | Line 1,071: | ||
| || | | || | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| symmetric relation || binary relation | |||
| || | | || | ||
| || | | || | ||
Line 849: | Line 1,085: | ||
| || | | || | ||
| || | | || | ||
| | | transitive relation || binary relation | ||
| || | | || | ||
| || | | || | ||
Line 856: | Line 1,092: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| well-founded relation || class; minimal element; empty set | |||
| || | | || | ||
| || | | || | ||
Line 866: | Line 1,102: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| well-order, well-order relation, well-ordering || | |||
| || | | || | ||
| || | | || | ||
Line 876: | Line 1,112: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
Line 885: | Line 1,120: | ||
| || | | || | ||
| || | | || | ||
| || | |||
|} | |||
{| class="wikitable sortable" | |||
|+ function | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | |||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | |||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | |||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | |||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | |||
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیشنیاز | |||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | |||
|- | |- | ||
| | | 函数 || | ||
| hán shù || | |||
| Funktion [f] || | |||
| function || binary relation; set | |||
| fonction [f] || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 906: | Line 1,155: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Boolean function || argument; Boolean domain <algebra> | |||
| || | | || | ||
| || | | || | ||
Line 916: | Line 1,165: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Boolean-valued function || function; value; Boolean domain <algebra> | |||
| || | | || | ||
| || | | || | ||
Line 926: | Line 1,175: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| complex-valued function || function; value; complex number | |||
| || | | || | ||
| || | | || | ||
Line 936: | Line 1,185: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| functions of several complex variables || argument; complex variable | |||
| || | | || | ||
| || | | || | ||
Line 946: | Line 1,195: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| function of several real variables, real multivariate function || argument; real variable | |||
| || | | || | ||
| || | | || | ||
Line 956: | Line 1,205: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| integer-valued function || function; value; integer | |||
| || | | || | ||
| || | | || | ||
Line 966: | Line 1,215: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| ordered pair || function | |||
| || | | || | ||
| || | | || | ||
Line 976: | Line 1,225: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| real-valued function || function; value; real number | |||
| || | | || | ||
| || | | || | ||
Line 1,007: | Line 1,246: | ||
|} | |} | ||
=== Axiomatic Set Theory === | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,019: | Line 1,258: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | |||
| || | |||
| || | | || | ||
| || | | || | ||
Line 1,039: | Line 1,268: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| amorphous set || infinite set; disjoint union; subset | |||
| || | | || | ||
| || | | || | ||
Line 1,049: | Line 1,278: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| normal function || ordinal number; monotonically increasing function | |||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
|} | |||
{| class="wikitable sortable" | |||
|+ axiom of choice | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | |||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | |||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | |||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | |||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | |||
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیشنیاز | |||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| axiom of choice || choice function | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
| || | | || | ||
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|- | |- | ||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
| || | | || | ||
|} | |||
|} | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ theorem in set theory | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,145: | Line 1,357: | ||
| || | | || | ||
| || | | || | ||
| theorem in set theory || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | |||
|- | |||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
Line 1,160: | Line 1,373: | ||
| || | | || | ||
| || | | || | ||
|- | |||
| 康托尔定理 || | |||
| Kāngtuō'ěr dìnglǐ || | |||
| Satz [m] von Cantor || | |||
| Cantor's theorem || power set; cardinality | |||
| théorème [m] de Cantor || | |||
| カントールの定理 || | |||
| カ↑ント↓ールの↑て↓いり || | |||
| || | | || | ||
| теоре́ма Ка́нтора || | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| well-ordering theorem, Zermelo's theorem || well-order | |||
| || | | || | ||
| || | | || | ||
Line 1,183: | Line 1,405: | ||
|} | |} | ||
== Proof Theory == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,195: | Line 1,417: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
| | | mathematical induction || | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
| | | sequent || | ||
| || | | || | ||
| || | | || | ||
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|} | |} | ||
== Model Theory == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,238: | Line 1,460: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
| | | elementary equivalence || structure; signature | ||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| signature || non-logical symbol <logic> | |||
| || | | || | ||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| structure || cardinality; arity | |||
| || | | || | ||
| || | | || | ||
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|} | |} | ||
== | == Computability Theory == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
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| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,332: | Line 1,544: | ||
|} | |} | ||
== | == Type Theory == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,354: | Line 1,566: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| boolean type || type | |||
| || | | || | ||
| || | | || | ||
Line 1,364: | Line 1,576: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| bottom type || type | |||
| || | | || | ||
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Line 1,374: | Line 1,586: | ||
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|- | |- | ||
| || | | || | ||
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| || | | || | ||
| identity type, propositional equality || equality; type | |||
| || | | || | ||
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Line 1,387: | Line 1,599: | ||
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| product type || type | |||
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Line 1,392: | Line 1,605: | ||
| || | | || | ||
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|- | |- | ||
| || | | || | ||
| || | | || | ||
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| | | unit type || type | ||
| || | | || | ||
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Line 1,428: | Line 1,627: | ||
|} | |} | ||
== | == Algebraic Logic == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
Line 1,448: | Line 1,646: | ||
| || | | || | ||
| || | | || | ||
| | |} | ||
| | === Boolean Algebra === | ||
{| class="wikitable sortable" | |||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | |||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | |||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | |||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | |||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | |||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | |||
|- | |||
| || | | || | ||
| || | | || | ||
Line 1,460: | Line 1,668: | ||
| || | | || | ||
|- | |- | ||
| | | 德摩根定律 || | ||
| | | Dé Mógēn dìnglǜ || | ||
| | | De-Morgansche Gesetze [n pl], De-Morgansche Regeln [f pl] || | ||
| De Morgan's laws || conjunction; disjunction; negation | |||
| lois [f pl] de De Morgan || | |||
| ド・モルガンの法則 || | |||
| ド・↑モルガ↓ンのほ↑うそく || | |||
| зако́ны де Мо́ргана, пра́вила де Мо́ргана || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| truth table || expression | |||
| table [f] de vérité || | |||
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|- | |- | ||
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|} | |||
<center> | |||
https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn3tab.svg/240px-Venn3tab.svg.png | |||
</center> | |||
|} | |||
{{Sci-Tech-Index-Menu}} | |||
{ | |||
==Other Lessons== | |||
* [[Language/Multiple-languages/Vocabulary/Longest-words|Longest words]] | |||
* [[Language/Multiple-languages/Vocabulary/Electromagnetism|Electromagnetism]] | |||
* [[Language/Multiple-languages/Vocabulary/Must‐Know-Words-for-Polyglots|Must‐Know Words for Polyglots]] | |||
* [[Language/Multiple-languages/Vocabulary/Similarities-between-French-and-Italian|Similarities between French and Italian]] | |||
* [[Language/Multiple-languages/Vocabulary/Statistics|Statistics]] | |||
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]] | |||
* [[Language/Multiple-languages/Vocabulary/I-love-you-in-all-languages|I love you in all languages]] | |||
* [[Language/Multiple-languages/Vocabulary/Emotions-in-many-languages|Emotions in many languages]] | |||
* [[Language/Multiple-languages/Vocabulary/Transparent-Words|Transparent Words]] | |||
* [[Language/Multiple-languages/Vocabulary/Musical-Notes-in-Many-Languages|Musical Notes in Many Languages]] | |||
<span links></span> |
Latest revision as of 13:15, 27 March 2023
Hello polyglots, 😀
On this page you will find a part of the Sci–Tech Index, a project for science and technology learners.
cmn-Hans-CN: 科目 | cmn-Latn.Pinyin-CN: kēmù | deu-Latn-DE: Fach [n] | eng-Latn-US: subject | fra-Latn-FR: matière [f] | jpn-Jpan-JP: 科目 | jpn-Hrkt-JP: か↑もく | pes-Aran-IR: رِشته | rus-Cyrl-RU: предме́т |
---|---|---|---|---|---|---|---|---|
集合论 | jíhé lùn | Mengenlehre [f] | set theory | théorie [f] des ensembles [m pl] | 集合論 | しゅ↑うご↓うろん | тео́рия мно́жеств | |
公理化集合论 | gǒnglǐhuà jíhélùn | axiomatische Mengenlehre | axiomatic set theory | théorie [f] axiomatique des ensembles [m pl] | 公理的集合論 | こ↑うりてき↓しゅ↑うご↓うろん | аксиомати́ческая тео́рия мно́жеств | |
证明论 | zhèngmíng lùn | Beweistheorie [f] | proof theory | théorie [f] de la démonstration, théorie [f] de la preuve | 証明論 | しょ↑うめ↓いろん | тео́рия доказа́тельств | |
模型论 | móxíng lùn | Modelltheorie [f] | model theory | théorie [f] des modèles [m pl] | モデル理論 | モ↑デルり↓ろん | тео́рия моде́лей | |
可计算性理论 | kějìsuànxìng lǐlùn | Berechenbarkeitstheorie [f], Rekursionstheorie [f] | computability theory, recursion theory | théorie [f] de la calculabilité | 計算可能性理論 | け↑いさんかのうせいり↓ろん | тео́рия вычисли́мости | |
类型论 | lèixíng lùn | Typentheorie [f] | type theory | théorie [f] des types [m pl] | 型理論 | か↑たり↓ろん | тео́рией ти́пов | |
代数逻辑 | dàishù luóji | algebraische Logik | algebraic logic | logique [f] algébrique | алгебраи́ческая ло́гика | |||
逻辑代数,布尔代数 | luóji dàishù, Bù'ěr dàishù | boolesche Algebra, boolescher Verband | Boolean algebra | algèbre [f] de Boole, algèbre booléenne | ブール代数,ブール束 | ブ↑ールだ↓いすう,ブ↑ールそく | а́лгебра ло́гики, а́лгебра выска́зываний | |
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
函数空间 | hánshù kōngjiān | Funktionenraum [m] | function space | set; function | espace fonctionnel | 関数空間 | か↑んすうく↓うかん | функциона́льное простра́нство | |||||||||
数学对象 | shùxué duìxiàng | mathematisches Objekt | mathematical object | objet [m] mathématique | 数学的対象 | す↑うがくてきた↓いしょう | математи́ческий объе́кт | ||||||||||
Set Theory[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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参数 | cān shù | Argument [m] | argument | function | argument [m] | 引数 | ひ↑きす↓う | аргуме́нт | |||||||||
双射 | shuāng shè | Bijektion [f], bijektive Funktion | bijection, bijective function, invertible function | function; set | bijection [f] | 全単射,双射 | ぜ↑んた↓んしゃ,そ↓うしゃ | бие́кция | |||||||||
二元运算 | èryuán yùnsuàn | zweistellige Verknüpfung, binäre Verknüpfung | binary operation, dyadic operation | operation | opération [f] binaire | 二項演算 | に↑こうえ↓んざん | бина́рная опера́ция, двуме́стная опера́ция | |||||||||
势,浓度 | shì, nóng dù | Mächtigkeit [f], Kardinalität [f] | cardinality | set | cardinalité [f] | 濃度,カーディナリティ | の↓うど,カ↑ーディナ↓リティ | мо́щность | |||||||||
基数 | jī shù | Kardinalzahl [f] | cardinal number, cardinal | cardinality | nombre cardinal, cardinal [m] | 基数 | き↑す↓う | кардина́льное число́ | |||||||||
笛卡尔积 | Díkǎ'ěr jī | kartesisches Produkt, Mengenprodukt [n] | Cartesian product | ordered pair | produit cartésien | 直積,デカルト積 | ちょ↑くせ↓き,デ↑カルトせ↓き | прямо́е произведе́ние, дека́ртово произведе́ние | |||||||||
选择函数 | xuǎnzé hánshù | Auswahlfunktion [f] | choice function | function; empty set; direct product <algebra> | fonction [f] de choix [m] | 選択関数 | せ↑んたくか↓んすう | фу́нкция вы́бора | |||||||||
类 | lèi | Klasse [f] | class | set | classe [f] | クラス,類 | ク↓ラス,る↓い | класс | |||||||||
到达域,陪域,上域,终域 | dàodá yù, péi yù, shàng yù, zhōng yù | Zielmenge [f], Wertevorrat [m] | codomain, set of destination | function | ensemble [m] d'arrivée [f] | 終域 | し↑ゅうい↓き | ||||||||||
连续统 | liánxù tǒng | Kontinuum [m] | continuum | cardinal number | continu [m] | 連続体 | れ↑んぞくたい | конти́нуум | |||||||||
定义域 | dìngyì yù | Definitionsmenge [f], Definitionsbereich [m] | domain, set of departure | function | ensemble [m] de définition [f] | 定義域 | て↑いぎ↓いき | о́бласть определе́ния | |||||||||
元素 | yuánsù | Element [n] | element | mathematical object | élément [m] | 元 | げ↓ん | элеме́нт | |||||||||
列举法 | lièjǔ fǎ | Aufzählung [f] | enumeration | set | énumération [f] | 数え上げ | か↑ぞえあげ | перечисле́ние | |||||||||
相等 | xiāng děng | Gleichheit [f] | equality | égalité [f] | 相等 | そ↑うとう | تَساوی | ра́венство | |||||||||
表达式,表示式,运算式 | biǎodá shì, biǎoshì shì, yùnsuàn shì | Ausdruck [m] | expression | digit; symbol | expression [f] | 数式 | す↑うしき | выраже́ние | |||||||||
外延性 | wàiyán xìng | Extensionalität [f] | extensionality, extensional equality | mathematical object | extensionnalité [f] | 外延性 | が↑いえんせい | экстенсиона́льность [ж] | |||||||||
单位元 | dānwèi yuán | neutrales Element | identity element, neutral element | binary operation; set | élément [m] neutre, élément [m] identité | 単位元,中立元 | た↑んいげ↓ん,ちゅ↑うりつげ↓ん | нейтра́льный элеме́нт | |||||||||
恒等函数 | héngděng hánshù | identische Abbildung | identity function, identity relation, identity map, identity transformation | argument | application [f] identité, fonction [f] identité | 恒等写像 | こ↑うとうしゃ↓ぞう | тожде́ственное отображе́ние | |||||||||
像 | xiàng | Bild [n], Bildbereich [m], Bildmenge [f] | image | function | image [f] | 像 | ぞ↓う | о́браз | |||||||||
族 | zú | Familie [f] | indexed family, family | set | famille | 族 | ぞ↑く | семе́йство, индекси́рованное семе́йство | |||||||||
不等 | bù děng | Ungleichheit [f] | inequality | equality | inégalité [f] | 不等 | ふ↑とう | нера́венство | |||||||||
单射 | dān shè | injektive Funktion | injection, injective function, one-to-one function | function; injectivity | injection [f] | 単射 | た↑んしゃ | инъе́кция, инъекти́вное отображе́ние | |||||||||
原像 | yuán xiàng | Urbild [n] | inverse image, preimage | codomain; subset | image [f] réciproque, préimage [f] | 逆像,原像 | ぎゃ↑くぞう,げ↑んぞう | обра́тный о́браз, проо́браз | |||||||||
映射 | yìngshè | Abbildung [f] | mapping | function | application [f] | 写像 | しゃ↑ぞう | отображе́ние | |||||||||
运算数,运算元 | yùnsuàn shù, yùnsuàn yuán | Operand [m] | operand | operation | opérande [m] | 被演算子 | ひ↑えんざ↓んし | опера́нд | |||||||||
运算 | yùnsuàn | Verknüpfung [f] | operation | opération [f] | 演算 | え↑んざん | oпера́ция | ||||||||||
序数 | xù shù | Ordinalzahl [f] | ordinal number | enumeration; ordinal numeral <linguistics> | nombre ordinal | 順序数 | じゅ↑んじょ↓すう | поря́дковым число́м, ордина́лом | |||||||||
值域 | zhí yù | Bild [n] (Funktion), Bildbereich [m] (Funktion), Bildmenge [f] (Funktion) | range | image | image [f] (application) | 値域 | ち↓いき | о́бласть значе́ний фу́нкции, мно́жество значе́ний фу́нкции | |||||||||
关系 | guānxi | Relation [f] | relation | set | relation [f] | 関係 | かんけい | отноше́ние | |||||||||
罗素悖论 | Luósù bèilùn | Russellsche Antinomie | Russell's paradox, Russell's antinomy | set | paradoxe [m] de Russell, antinomie [f] de Russell | ラッセルのパラドックス | ラ↓ッセルのパ↑ラド↓ックス | парадо́кс Ра́ссела, антино́мия Ра́ссела | |||||||||
集合,集 | jíhé, jí | Menge [f] | set | element | ensemble [m] | 集合 | しゅ↑うごう | мно́жество | |||||||||
满射 | mǎn shè | surjektive Funktion | surjection, surjective function, onto function | function | surjection [f], application surjective | 全射 | ぜ↑んしゃ | сюръе́кция, сюръекти́вное отображе́ние | |||||||||
对称差 | duìchèn chā | symmetrische Differenz | symmetric difference, disjunctive union | intersection | différence [f] symétrique | 対称差 | た↑いしょうさ | симметри́ческая ра́зность | |||||||||
多元组 | duōyuán zǔ | Tupel [n] | tuple | element; sequence <number theory> | uplet [m] | 順序組,組 | じゅ↑んじょぐみ,く↑み | корте́ж | |||||||||
全集 | quán jí | Universalmenge [f], Allmenge [f], Grundmenge [f] | universal set | universe | ensemble référentiel | 全体集合,普遍集合 | ぜ↑んたいしゅ↓うごう,ふ↑へんしゅ↓うごう | универса́льное мно́жество | |||||||||
全类 | quán lèi | Universum [n] | universe | class | univers [m] | 宇宙 | う↓ちゅう | универса́льный класс | |||||||||
基本元素 | jīběn yuánsù | Urelement [n] | urelement | set | ur-element [m] | урэлеме́нт | |||||||||||
范恩图,维恩图,韦恩图,文氏图 | Fàn'ēn tú, Wéi'ēn tú, Wéi'ēn tú, Wénshì tú | Venn-Diagramm [n] | Venn diagram | set | diagramme [m] de Venn | ベン図,ヴェン図 | ベ↓ンず、ヴェ↓ンず | диагра́мма Ве́нна | |||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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property of binary operation | |||||||||||||||||
反交换律 | fǎnjiāohuàn lǜ | Antikommutativgesetz [n], Antikommutativität [f] | anticommutative property, anticommutativity | operation | |||||||||||||
结合律 | jiéhé lǜ | Assoziativgesetz [n], Assoziativität [f] | associative property, associativity | operation | |||||||||||||
交换律 | jiāohuàn lǜ | Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f] | commutative property, commutativity | operation | |||||||||||||
分配律 | fēnpèi lǜ | Distributivgesetz [n], Distributivität [f] | distributive property, distributivity | operation | |||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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operation on set | |||||||||||||||||
absolute complement | complement; subset | ||||||||||||||||
补集 | bǔ jí | Komplement [n] | complement, set difference | set | complémentaire [m] | 差集合 | さ↑しゅ↓うごう | ра́зность мно́жеств | |||||||||
intersection | set | ||||||||||||||||
power set, powerset | subset; empty set | ||||||||||||||||
relative complement | complement; subset | ||||||||||||||||
union | set | ||||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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system of set theory | |||||||||||||||||
Zermelo–Fraenkel set theory | axiomatic system | ||||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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type of set | |||||||||||||||||
countable set | subset; cardinality | ||||||||||||||||
empty set | set | ||||||||||||||||
finite set | set | ||||||||||||||||
fuzzy set, uncertain set | set | ||||||||||||||||
infinite set | set | ||||||||||||||||
proper subset | subset | ||||||||||||||||
singleton. unit set | set | ||||||||||||||||
subset | set | ||||||||||||||||
superset | set | ||||||||||||||||
transitive set | subset; urelement | ||||||||||||||||
universal set | mathematical object | ||||||||||||||||
unordered pair, pair set | set | ||||||||||||||||
well-founded set | transitive closure | ||||||||||||||||
well-ordered set | well-order; total order; non-empty set; least element | ||||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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二元关系 | èryuán guānxi | binäre Relation | binary relation | relation | relation [f] binaire | ||||||||||||
connected relation, total relation | binary relation | ||||||||||||||||
converse relation | binary relation | ||||||||||||||||
equivalence relation | reflexive relation; symmetric relation; transitive relation | ||||||||||||||||
finitary relation | Cartesian product | ||||||||||||||||
symmetric relation | binary relation | ||||||||||||||||
transitive relation | binary relation | ||||||||||||||||
well-founded relation | class; minimal element; empty set | ||||||||||||||||
well-order, well-order relation, well-ordering | |||||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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函数 | hán shù | Funktion [f] | function | binary relation; set | fonction [f] | ||||||||||||
Boolean function | argument; Boolean domain <algebra> | ||||||||||||||||
Boolean-valued function | function; value; Boolean domain <algebra> | ||||||||||||||||
complex-valued function | function; value; complex number | ||||||||||||||||
functions of several complex variables | argument; complex variable | ||||||||||||||||
function of several real variables, real multivariate function | argument; real variable | ||||||||||||||||
integer-valued function | function; value; integer | ||||||||||||||||
ordered pair | function | ||||||||||||||||
real-valued function | function; value; real number | ||||||||||||||||
Axiomatic Set Theory[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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amorphous set | infinite set; disjoint union; subset | ||||||||||||||||
normal function | ordinal number; monotonically increasing function | ||||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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axiom of choice | choice function | ||||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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theorem in set theory | |||||||||||||||||
康托尔定理 | Kāngtuō'ěr dìnglǐ | Satz [m] von Cantor | Cantor's theorem | power set; cardinality | théorème [m] de Cantor | カントールの定理 | カ↑ント↓ールの↑て↓いり | теоре́ма Ка́нтора | |||||||||
well-ordering theorem, Zermelo's theorem | well-order | ||||||||||||||||
Proof Theory[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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mathematical induction | |||||||||||||||||
sequent |
Model Theory[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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elementary equivalence | structure; signature | ||||||||||||||||
signature | non-logical symbol <logic> | ||||||||||||||||
structure | cardinality; arity | ||||||||||||||||
Computability Theory[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Type Theory[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | pes-Aran-IR: مَفهوم | pes-Aran-IR: پیشنیاز | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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boolean type | type | ||||||||||||||||
bottom type | type | ||||||||||||||||
identity type, propositional equality | equality; type | ||||||||||||||||
product type | type | ||||||||||||||||
unit type | type | ||||||||||||||||
Algebraic Logic[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Boolean Algebra[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
德摩根定律 | Dé Mógēn dìnglǜ | De-Morgansche Gesetze [n pl], De-Morgansche Regeln [f pl] | De Morgan's laws | conjunction; disjunction; negation | lois [f pl] de De Morgan | ド・モルガンの法則 | ド・↑モルガ↓ンのほ↑うそく | зако́ны де Мо́ргана, пра́вила де Мо́ргана | |||||||
truth table | expression | table [f] de vérité | |||||||||||||
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