Difference between revisions of "Language/Multiple-languages/Vocabulary/Mathematical-Logic"
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| boolesche Algebra, boolescher Verband | | boolesche Algebra, boolescher Verband | ||
| Boolean algebra | | Boolean algebra | ||
| algèbre [f] de Boole, algèbre booléenne | | algèbre [f] de Boole, algèbre booléenne | ||
| ブール代数,ブール束 | | ブール代数,ブール束 | ||
| ブ↑ールだ↓いすう,ブ↑ールそく | | ブ↑ールだ↓いすう,ブ↑ールそく | ||
Line 113: | Line 113: | ||
|} | |} | ||
{| 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 | ||
Line 166: | 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 | ||
Line 196: | Line 195: | ||
| ひ↑きす↓う || | | ひ↑きす↓う || | ||
| || | | || | ||
| | | аргуме́нт || | ||
|- | |- | ||
| 双射 || | | 双射 || | ||
Line 274: | Line 273: | ||
| 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 || | ||
Line 323: | Line 322: | ||
| equality || | | 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 || | ||
Line 342: | Line 341: | ||
| Extensionalität [f] || | | Extensionalität [f] || | ||
| extensionality, extensional equality || mathematical object | | extensionality, extensional equality || mathematical object | ||
| | | extensionnalité [f] || | ||
| 外延性 || | | 外延性 || | ||
| が↑いえんせい || | | が↑いえんせい || | ||
| || | | || | ||
| | | экстенсиона́льность [ж] || | ||
|- | |- | ||
| | | 单位元 || | ||
| | | dānwèi yuán || | ||
| | | neutrales Element || | ||
| identity element, neutral element || binary operation; set | | 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 || | |||
|- | |||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|} | |||
{| 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 || | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
| | | || | ||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
| | | 反交换律 || | ||
| | | fǎnjiāohuàn lǜ || | ||
| | | Antikommutativgesetz [n], Antikommutativität [f] || | ||
| | | anticommutative property, anticommutativity || operation | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
| | | 结合律 || | ||
| | | jiéhé lǜ || | ||
| | | Assoziativgesetz [n], Assoziativität [f] || | ||
| | | associative property, associativity || operation | ||
| || | | || | ||
| || | | || | ||
Line 438: | Line 630: | ||
| || | | || | ||
|- | |- | ||
| | | 交换律 || | ||
| | | jiāohuàn lǜ || | ||
| | | Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f] || | ||
| | | commutative property, commutativity || operation | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
| 分配律 || | |||
| fēnpèi lǜ || | |||
| Distributivgesetz [n], Distributivität [f] || | |||
| distributive property, distributivity || operation | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
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|} | |||
{| 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 || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | |- | ||
| || | | || | ||
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| || | | || | ||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| 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 | ||
| || | | || | ||
| || | | || | ||
Line 521: | Line 726: | ||
| || | | || | ||
| || | | || | ||
| | | power set, powerset || subset; empty set | ||
| || | | || | ||
| || | | || | ||
Line 531: | Line 736: | ||
| || | | || | ||
| || | | || | ||
| | | relative complement || complement; subset | ||
| || | | || | ||
| || | | || | ||
Line 541: | Line 746: | ||
| || | | || | ||
| || | | || | ||
| | | union || set | ||
| || | | || | ||
| || | | || | ||
Line 551: | Line 756: | ||
| || | | || | ||
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Line 557: | Line 761: | ||
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|} | |||
|} | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ | |+ system of 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 | ||
Line 594: | Line 779: | ||
| || | | || | ||
| || | | || | ||
| | | system of set theory || | ||
| || | | || | ||
| || | | || | ||
Line 611: | Line 796: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | Zermelo–Fraenkel set theory || axiomatic system | ||
| || | | || | ||
| || | | || | ||
Line 663: | 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 | ||
Line 677: | Line 832: | ||
| || | | || | ||
| || | | || | ||
| | | type of set || | ||
| || | | || | ||
| || | | || | ||
Line 697: | Line 852: | ||
| || | | || | ||
| || | | || | ||
| | | countable set || subset; cardinality | ||
| || | | || | ||
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Line 703: | Line 858: | ||
| || | | || | ||
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|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | empty set || set | ||
| || | | || | ||
| || | | || | ||
Line 727: | Line 872: | ||
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| | | finite set || set | ||
| || | | || | ||
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Line 737: | Line 882: | ||
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| | | fuzzy set, uncertain set || set | ||
| || | | || | ||
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Line 747: | Line 892: | ||
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| | | infinite set || set | ||
| || | | || | ||
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Line 757: | Line 902: | ||
| || | | || | ||
| || | | || | ||
| proper subset || subset | |||
| || | | || | ||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| singleton. unit set || set | |||
| || | | || | ||
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Line 763: | Line 918: | ||
| || | | || | ||
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|- | |- | ||
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| | | subset || set | ||
| || | | || | ||
| || | | || | ||
Line 790: | Line 932: | ||
| || | | || | ||
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| | | superset || set | ||
| || | | || | ||
| || | | || | ||
Line 800: | Line 942: | ||
| || | | || | ||
| || | | || | ||
| | | transitive set || subset; urelement | ||
| || | | || | ||
| || | | || | ||
Line 810: | Line 952: | ||
| || | | || | ||
| || | | || | ||
| universal set || mathematical object | |||
| || | | || | ||
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| || | | || | ||
| || | | || | ||
| || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | unordered pair, pair set || set | ||
| | |||
| || | | || | ||
| || | | || | ||
Line 843: | Line 972: | ||
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| || | | || | ||
| | | well-founded set || transitive closure | ||
| || | | || | ||
| || | | || | ||
Line 853: | Line 982: | ||
| || | | || | ||
| || | | || | ||
| | | well-ordered set || well-order; total order; non-empty set; least element | ||
| || | | || | ||
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Line 863: | Line 992: | ||
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Line 869: | Line 997: | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | |} | ||
| | |||
| | {| class="wikitable sortable" | ||
|+ binary relation | |||
! 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 | |||
|- | |||
| 二元关系 || | |||
| èryuán guānxi || | |||
| binäre Relation || | |||
| binary relation || relation | |||
| relation [f] binaire || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
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| || | | || | ||
Line 893: | Line 1,035: | ||
| || | | || | ||
| || | | || | ||
| | | connected relation, total relation || binary relation | ||
| || | | || | ||
| || | | || | ||
Line 903: | Line 1,045: | ||
| || | | || | ||
| || | | || | ||
| | | converse relation || binary relation | ||
| || | | || | ||
| || | | || | ||
Line 913: | Line 1,055: | ||
| || | | || | ||
| || | | || | ||
| | | equivalence relation || reflexive relation; symmetric relation; transitive relation | ||
| || | | || | ||
| || | | || | ||
Line 923: | Line 1,065: | ||
| || | | || | ||
| || | | || | ||
| | | finitary relation || Cartesian product | ||
| || | | || | ||
| || | | || | ||
Line 933: | Line 1,075: | ||
| || | | || | ||
| || | | || | ||
| | | symmetric relation || binary relation | ||
| || | | || | ||
| || | | || | ||
Line 943: | Line 1,085: | ||
| || | | || | ||
| || | | || | ||
| transitive | | transitive relation || binary relation | ||
| || | | || | ||
| || | | || | ||
Line 953: | Line 1,095: | ||
| || | | || | ||
| || | | || | ||
| | | well-founded relation || class; minimal element; empty set | ||
| || | | || | ||
| || | | || | ||
Line 963: | Line 1,105: | ||
| || | | || | ||
| || | | || | ||
| | | well-order, well-order relation, well-ordering || | ||
| || | | || | ||
| || | | || | ||
Line 973: | Line 1,115: | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
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Line 979: | 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 995: | Line 1,154: | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Boolean function || argument; Boolean domain <algebra> | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,026: | Line 1,168: | ||
| || | | || | ||
| || | | || | ||
| | | Boolean-valued function || function; value; Boolean domain <algebra> | ||
| || | | || | ||
| || | | || | ||
Line 1,036: | Line 1,178: | ||
| || | | || | ||
| || | | || | ||
| | | complex-valued function || function; value; complex number | ||
| || | | || | ||
| || | | || | ||
Line 1,046: | Line 1,188: | ||
| || | | || | ||
| || | | || | ||
| | | functions of several complex variables || argument; complex variable | ||
| || | | || | ||
| || | | || | ||
Line 1,056: | Line 1,198: | ||
| || | | || | ||
| || | | || | ||
| | | function of several real variables, real multivariate function || argument; real variable | ||
| || | | || | ||
| || | | || | ||
Line 1,066: | Line 1,208: | ||
| || | | || | ||
| || | | || | ||
| | | integer-valued function || function; value; integer | ||
| || | | || | ||
| || | | || | ||
Line 1,076: | Line 1,218: | ||
| || | | || | ||
| || | | || | ||
| | | ordered pair || function | ||
| || | | || | ||
| || | | || | ||
Line 1,086: | Line 1,228: | ||
| || | | || | ||
| || | | || | ||
| | | real-valued function || function; value; real number | ||
| || | | || | ||
| || | | || | ||
Line 1,096: | Line 1,238: | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,102: | Line 1,243: | ||
| || | | || | ||
| || | | || | ||
| || | |||
|} | |||
=== Axiomatic Set Theory === | |||
{| 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 | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | || | ||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| amorphous set || infinite set; disjoint union; subset | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| normal function || ordinal number; monotonically increasing function | |||
| || | | || | ||
| || | | || | ||
Line 1,125: | Line 1,300: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ | |+ axiom of choice | ||
! 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 | ||
Line 1,136: | Line 1,311: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| axiom of choice || choice function | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
| || | | || | ||
Line 1,155: | Line 1,326: | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,175: | Line 1,340: | ||
| || | | || | ||
| || | | || | ||
|} | |||
{| class="wikitable sortable" | |||
|+ theorem in 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 | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | theorem in set theory || | ||
| || | | || | ||
| || | | || | ||
Line 1,189: | Line 1,367: | ||
| || | | || | ||
| || | | || | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,196: | Line 1,374: | ||
| || | | || | ||
|- | |- | ||
| 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 1,209: | Line 1,397: | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,215: | Line 1,402: | ||
| || | | || | ||
| || | | || | ||
| || | |||
|} | |||
== Proof Theory == | |||
{| 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 | |||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,229: | Line 1,430: | ||
| || | | || | ||
| || | | || | ||
| | | mathematical induction || | ||
| || | | || | ||
| || | | || | ||
Line 1,239: | Line 1,440: | ||
| || | | || | ||
| || | | || | ||
| | | sequent || | ||
| || | | || | ||
| || | | || | ||
Line 1,247: | Line 1,448: | ||
|} | |} | ||
== | == 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 | ||
Line 1,272: | Line 1,473: | ||
| || | | || | ||
| || | | || | ||
| | | elementary equivalence || structure; signature | ||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| signature || non-logical symbol <logic> | |||
| || | | || | ||
| || | | || | ||
Line 1,282: | Line 1,493: | ||
| || | | || | ||
| || | | || | ||
| | | structure || cardinality; arity | ||
| || | | || | ||
| || | | || | ||
Line 1,300: | Line 1,511: | ||
|} | |} | ||
== 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 | ||
Line 1,315: | Line 1,526: | ||
| || | | || | ||
| || | | || | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,331: | Line 1,542: | ||
| || | | || | ||
| || | | || | ||
| | |} | ||
== 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 | ||
Line 1,358: | Line 1,559: | ||
| || | | || | ||
| || | | || | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,368: | Line 1,569: | ||
| || | | || | ||
| || | | || | ||
| boolean type || type | |||
| || | | || | ||
| || | | || | ||
Line 1,373: | Line 1,575: | ||
| || | | || | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | bottom type || type | ||
| || | | || | ||
| || | | || | ||
Line 1,398: | Line 1,589: | ||
| || | | || | ||
| || | | || | ||
| identity type, propositional equality || equality; type | |||
| || | | || | ||
| || | | || | ||
Line 1,403: | Line 1,595: | ||
| || | | || | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| | | product type || type | ||
| || | | || | ||
| || | | || | ||
Line 1,431: | Line 1,609: | ||
| || | | || | ||
| || | | || | ||
| | | unit type || type | ||
| || | | || | ||
| || | | || | ||
Line 1,441: | Line 1,619: | ||
| || | | || | ||
| || | | || | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,449: | 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 | ||
Line 1,458: | Line 1,636: | ||
! 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 1,469: | 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 1,480: | Line 1,665: | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |||
| 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 || | |||
| || | | || | ||
| || | | || | ||
Line 1,494: | Line 1,689: | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,500: | Line 1,694: | ||
| || | | || | ||
| || | | || | ||
|} | |||
<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 |
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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 | ||||||||||
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 |
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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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