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== Main ==
{| 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
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|}
|}


== Set Theory ==
=== 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
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| ひ↑きす↓う ||  
| ひ↑きす↓う ||  
|  ||  
|  ||  
| аргуме́нт ||  
| аксиомати́ческая тео́рия мно́жеств ||  
|-
|-
| 双射 ||  
| 双射 ||  
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| ensemble [m] d'arrivée [f] ||  
| ensemble [m] d'arrivée [f] ||  
| 終域 ||  
| 終域 ||  
| し↑ゅうい↓き ||
| しゅういき ||  
|  ||  
|  ||  
|  ||  
| о́бласть значе́ний ||
|-
|-
| 连续统 ||  
| 连续统 ||  
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| 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 341: Line 342:
| 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 ||
| identity function, identity relation, identity map, identity transformation || argument
|-
| 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 ||  
| image || function; set
|-
| ||  
| 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 ||  
| ||
|  ||
| indexed family, family || set
|  ||
|  ||
|  ||
|  ||
|  ||  
|-
|-
| 全类 ||  
| 不等 ||  
| quán lèi ||  
| bù děng ||  
| Universum [n] ||  
| Ungleichheit [f] ||  
| universe || class
| inequality || equality
| univers [m] ||
| inégalité [f] ||  
| 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 ||  
| ||  
|-
| ||
| injection, injective function, one-to-one function || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|-
|  ||
|  ||
|  ||
| inverse image, preimage || codomain; subset
|  ||  
|  ||  
|  ||  
|  ||  
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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 ||  
| mapping || function
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| 运算数，运算元 ||
| yùnsuàn shù, yùnsuàn yuán ||
| Operand [m] ||
| operand || operation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|-
| 运算 ||
| yùnsuàn ||
| Verknüpfung [f] ||
| operation ||
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| 反交换律 ||
| fǎnjiāohuàn lǜ ||
| Antikommutativgesetz [n], Antikommutativität [f] ||
| anticommutative property, anticommutativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
| ordinal number || enumeration; ordinal numeral <linguistics>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
| 结合律 ||
| jiéhé lǜ ||
| Assoziativgesetz [n], Assoziativität [f] ||
| associative property, associativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
| range || codomain; image
| 交换律 ||
| jiāohuàn lǜ ||
| Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f] ||
| commutative property, commutativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| 分配律 ||  
| 关系 ||  
| fēnpèi lǜ ||  
| guānxi ||  
| Distributivgesetz [n], Distributivität [f] ||  
| Relation [f] ||  
| distributive property, distributivity || operation
| relation || set
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| Russell's paradox, Russell's antinomy || set
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| set || element
|  ||  
|  ||  
|  ||  
|  ||  
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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 ||  
| surjection, surjective function, onto function || function
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| ||  
| symmetric difference, disjunctive union || intersection
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| absolute complement || complement; subset
| tree || partially ordered set; well-ordered set
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| 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
| tuple || element; sequence <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| power set, powerset || subset; empty set
| universe ||  
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| relative complement || complement; subset
| urelement || set
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| union || set
| Venn diagram || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 765: Line 580:


{| class="wikitable sortable"
{| class="wikitable sortable"
|+ system of set theory
|+ property of binary operation
! 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 779: Line 594:
|  ||  
|  ||  
|  ||  
|  ||  
| system of set theory ||  
| property of binary operation ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 796: Line 611:
|  ||  
|  ||  
|-
|-
| 反交换律 ||
| fǎnjiāohuàn lǜ ||
| Antikommutativgesetz [n], Antikommutativität [f] ||
| anticommutative property, anticommutativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Zermelo–Fraenkel set theory || axiomatic system
| ||  
|  ||
|-
| 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
|  ||  
|  ||  
|  ||  
|  ||  
Line 818: Line 663:


{| class="wikitable sortable"
{| class="wikitable sortable"
|+ type of set
|+ operation on 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 832: Line 677:
|  ||  
|  ||  
|  ||  
|  ||  
| type of set ||  
| operation on set ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 852: Line 697:
|  ||  
|  ||  
|  ||  
|  ||  
| countable set || subset; cardinality
| absolute complement || complement; subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 859: Line 704:
|  ||  
|  ||  
|-
|-
| 补集 ||
| bǔ jí ||
| Komplement [n] ||
| complement, set difference || set
| complémentaire [m] ||
| 差集合 ||
| さ↑しゅ↓うごう ||
|  ||  
|  ||  
| ра́зность мно́жеств ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
| empty set || set
| ||
| intersection || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 872: Line 727:
|  ||  
|  ||  
|  ||  
|  ||  
| finite set || set
| power set, powerset || subset; empty set
|  ||  
|  ||  
|  ||  
|  ||  
Line 882: Line 737:
|  ||  
|  ||  
|  ||  
|  ||  
| fuzzy set, uncertain set || set
| relative complement || complement; subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 892: Line 747:
|  ||  
|  ||  
|  ||  
|  ||  
| infinite set || set
| union || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 901: Line 756:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
| proper subset || subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| singleton. unit set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 918: Line 763:
|  ||  
|  ||  
|  ||  
|  ||  
|}
{| 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
|-
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| subset || set
| system of set theory ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 932: Line 790:
|  ||  
|  ||  
|  ||  
|  ||  
| superset || set
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 942: Line 800:
|  ||  
|  ||  
|  ||  
|  ||  
| transitive set || subset; urelement
| Zermelo–Fraenkel set theory || axiomatic system
|  ||  
|  ||  
|  ||  
|  ||  
Line 952: Line 810:
|  ||  
|  ||  
|  ||  
|  ||  
| universal set || mathematical object
|  ||  
|  ||  
|  ||  
|  ||  
Line 958: Line 815:
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|}
{| class="wikitable sortable"
|+ type of 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
|-
|  ||  
|  ||  
|  ||  
|  ||  
| unordered pair, pair set || set
| ||
| type of set ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 972: Line 843:
|  ||  
|  ||  
|  ||  
|  ||  
| well-founded set || transitive closure
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 982: Line 853:
|  ||  
|  ||  
|  ||  
|  ||  
| well-ordered set || well-order; total order; non-empty set; least element
| countable set || subset; cardinality
|  ||  
|  ||  
|  ||  
|  ||  
Line 990: Line 861:
|-
|-
|  ||  
|  ||  
|  ||
|  ||
| empty set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 995: Line 869:
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
| finite set || set
 
| ||  
{| 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 ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,025: Line 883:
|  ||  
|  ||  
|  ||  
|  ||  
| ||  
| fuzzy set, uncertain set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,035: Line 893:
|  ||  
|  ||  
|  ||  
|  ||  
| connected relation, total relation || binary relation
| infinite set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,045: Line 903:
|  ||  
|  ||  
|  ||  
|  ||  
| converse relation || binary relation
| proper subset || subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,055: Line 913:
|  ||  
|  ||  
|  ||  
|  ||  
| equivalence relation || reflexive relation; symmetric relation; transitive relation
| singleton. unit set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,065: Line 923:
|  ||  
|  ||  
|  ||  
|  ||  
| finitary relation || Cartesian product
| subset || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,075: Line 933:
|  ||  
|  ||  
|  ||  
|  ||  
| symmetric relation || binary relation
| superset || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,085: Line 943:
|  ||  
|  ||  
|  ||  
|  ||  
| transitive relation || binary relation
| transitive set || subset; urelement
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,095: Line 953:
|  ||  
|  ||  
|  ||  
|  ||  
| well-founded relation || class; minimal element; empty set
| universal set || mathematical object
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,105: Line 963:
|  ||  
|  ||  
|  ||  
|  ||  
| well-order, well-order relation, well-ordering ||  
| unordered pair, pair set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,115: Line 973:
|  ||  
|  ||  
|  ||  
|  ||  
| well-founded set || transitive closure
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| well-ordered set || well-order; total order; non-empty set; least element
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
{| 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 1,150: Line 995:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|}
{| 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 ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,158: Line 1,026:
|  ||  
|  ||  
|  ||  
|  ||  
| Boolean function || argument; Boolean domain <algebra>
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,168: Line 1,036:
|  ||  
|  ||  
|  ||  
|  ||  
| Boolean-valued function || function; value; Boolean domain <algebra>
| connected relation, total relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,178: Line 1,046:
|  ||  
|  ||  
|  ||  
|  ||  
| complex-valued function || function; value; complex number
| converse relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,188: Line 1,056:
|  ||  
|  ||  
|  ||  
|  ||  
| functions of several complex variables || argument; complex variable
| equivalence relation || reflexive relation; symmetric relation; transitive relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,198: Line 1,066:
|  ||  
|  ||  
|  ||  
|  ||  
| function of several real variables, real multivariate function || argument; real variable
| finitary relation || Cartesian product
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,208: Line 1,076:
|  ||  
|  ||  
|  ||  
|  ||  
| integer-valued function || function; value; integer
| symmetric relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,218: Line 1,086:
|  ||  
|  ||  
|  ||  
|  ||  
| ordered pair || function
| transitive relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,228: Line 1,096:
|  ||  
|  ||  
|  ||  
|  ||  
| real-valued function || function; value; real number
| well-founded relation || class; minimal element; empty set
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| well-order, well-order relation, well-ordering ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,246: Line 1,124:
|}
|}


=== Axiomatic Set Theory ===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ function
! 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 1,257: Line 1,135:
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
| 函数 ||
| hán shù ||
| Funktion [f] ||
| function || binary relation; set
| fonction [f] ||
|  ||
|  ||
|  ||
|  ||
|-
|-
|  ||  
|  ||  
Line 1,271: Line 1,159:
|  ||  
|  ||  
|  ||  
|  ||  
| amorphous set || infinite set; disjoint union; subset
| Boolean function || argument; Boolean domain <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,281: Line 1,169:
|  ||  
|  ||  
|  ||  
|  ||  
| normal function || ordinal number; monotonically increasing function
| Boolean-valued function || function; value; Boolean domain <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,291: Line 1,179:
|  ||  
|  ||  
|  ||  
|  ||  
| complex-valued function || function; value; complex number
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| functions of several complex variables || argument; complex variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,297: Line 1,195:
|  ||  
|  ||  
|  ||  
|  ||  
|}
{| 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
| function of several real variables, real multivariate function || argument; real variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,324: Line 1,209:
|  ||  
|  ||  
|  ||  
|  ||  
| integer-valued function || function; value; integer
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,329: Line 1,215:
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|-
|  ||
|  ||
| ordered pair || function
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| real-valued function || function; value; real number
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,342: Line 1,247:
|}
|}


==== Axiomatic Set Theory ====
{| 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
Line 1,357: Line 1,262:
|  ||  
|  ||  
|  ||  
|  ||  
| theorem in set theory ||  
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,367: Line 1,272:
|  ||  
|  ||  
|  ||  
|  ||  
| amorphous set || infinite set; disjoint union; subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
| normal function || ordinal number; monotonically increasing function
| 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 1,405: Line 1,300:
|}
|}


== Proof Theory ==
{| 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 1,420: Line 1,315:
|  ||  
|  ||  
|  ||  
|  ||  
| axiom of choice || choice function
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,425: Line 1,321:
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| mathematical induction ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,440: Line 1,335:
|  ||  
|  ||  
|  ||  
|  ||  
| sequent ||  
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,448: Line 1,343:
|}
|}


== Model Theory ==
{| 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
Line 1,463: Line 1,358:
|  ||  
|  ||  
|  ||  
|  ||  
| theorem in set theory ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,468: Line 1,364:
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| elementary equivalence || structure; signature
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,480: Line 1,375:
|  ||  
|  ||  
|-
|-
| 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 ||  
|  ||
| signature || non-logical symbol <logic>
|  ||
|  ||
|  ||
|  ||
|  ||  
|-
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| structure || cardinality; arity
| well-ordering theorem, Zermelo's theorem || well-order
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,511: Line 1,406:
|}
|}


== Computability Theory ==
=== 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
Line 1,536: Line 1,431:
|  ||  
|  ||  
|  ||  
|  ||  
| mathematical induction ||
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| sequent ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,544: Line 1,449:
|}
|}


== Type Theory ==
=== 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 1,569: Line 1,474:
|  ||  
|  ||  
|  ||  
|  ||  
| boolean type || type
| elementary equivalence || structure; signature
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,579: Line 1,484:
|  ||  
|  ||  
|  ||  
|  ||  
| bottom type || type
| signature || non-logical symbol <logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,589: Line 1,494:
|  ||  
|  ||  
|  ||  
|  ||  
| identity type, propositional equality || equality; type
| structure || cardinality; arity
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,599: Line 1,504:
|  ||  
|  ||  
|  ||  
|  ||  
| product type || type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,605: Line 1,509:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
=== Computability 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
|-
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| unit type || type
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,627: Line 1,545:
|}
|}


== Algebraic Logic ==
=== 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
Line 1,636: Line 1,554:
! 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
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
Line 1,646: Line 1,565:
|  ||  
|  ||  
|  ||  
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|}
=== 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
|-
|  ||  
|  ||  
|-
|  ||
|  ||
|  ||
| boolean type || type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,665: Line 1,576:
|  ||  
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|-
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|  ||  
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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 ||
|-
|  ||  
|  ||  
| bottom type || type
|  ||  
|  ||  
|  ||  
|  ||  
| truth table || expression
| table [f] de vérité ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,689: Line 1,590:
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| identity type, propositional equality || equality; type
|  ||  
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Line 1,694: Line 1,596:
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|}
|-
 
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<center>
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn3tab.svg/240px-Venn3tab.svg.png
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</center>
| product type || type
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|-
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| unit type || type
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|-
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|}


{{Sci-Tech-Index-Menu}}
=== Algebraic Logic ===
{| 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
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}


==Other Lessons==
==== Boolean Algebra ====
* [[Language/Multiple-languages/Vocabulary/Longest-words|Longest words]]
{| class="wikitable sortable"
* [[Language/Multiple-languages/Vocabulary/Electromagnetism|Electromagnetism]]
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
* [[Language/Multiple-languages/Vocabulary/Must‐Know-Words-for-Polyglots|Must‐Know Words for Polyglots]]
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
* [[Language/Multiple-languages/Vocabulary/Similarities-between-French-and-Italian|Similarities between French and Italian]]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
* [[Language/Multiple-languages/Vocabulary/Statistics|Statistics]]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
* [[Language/Multiple-languages/Vocabulary/I-love-you-in-all-languages|I love you in all languages]]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
* [[Language/Multiple-languages/Vocabulary/Emotions-in-many-languages|Emotions in many languages]]
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
* [[Language/Multiple-languages/Vocabulary/Transparent-Words|Transparent Words]]
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
* [[Language/Multiple-languages/Vocabulary/Musical-Notes-in-Many-Languages|Musical Notes in Many Languages]]
|-
<span links></span>
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
| 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 ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
== Appendix ==
=== Sentence ===
{| 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
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
=== Symbol ===
==== Set Theory ====
{| class="wikitable sortable"
! symbol
! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! eng-Latn-US: concept
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 概念
! jpn-Hrkt-JP: が↓いねん
! pes-Aran-IR: مَفهوم
! rus-Cyrl-RU: конце́пция
|-
|
|
|
|
|
|
|
|
|
|
|-
| =
|
|
|
| is equal to
|
|
|
|
|
|-
| ≠
|
|
|
| is not equal to
|
|
|
|
|
|-
| ∈
|
|
|
| is element of
|
|
|
|
|
|-
| ∉
|
|
|
| is not element of
|
|
|
|
|
|-
| ∋
|
|
|
| contains member
|
|
|
|
|
|-
| ∌
|
|
|
| does not contain member
|
|
|
|
|
|-
| ⊂
|
|
|
| is subset of; is proper subset of
|
|
|
|
|
|-
| ⊃
|
|
|
| is superset of; is proper superset of
|
|
|
|
|
|-
| ⊆
|
|
|
| is subset of
|
|
|
|
|
|-
| ⊇
|
|
|
| is superset of
|
|
|
|
|
|-
| ⊄
|
|
|
| is not subset of; is not proper subset of
|
|
|
|
|
|-
| ⊅
|
|
|
| is not superset of; is not proper superset of
|
|
|
|
|
|-
| ⊈
|
|
|
| is not subset of
|
|
|
|
|
|-
| ⊉
|
|
|
| is not superset of
|
|
|
|
|
|-
| ⊊
|
|
|
| is subset and not proper subset of
|
|
|
|
|
|-
| ⊋
|
|
|
| is superset and not proper superset of
|
|
|
|
|
|-
| ''A'', ''B'', ''C'', ...
|
|
|
| set
|
|
|
|
|
|-
| ''a'', ''b'', ''c'', ...
|
|
|
| element
|
|
|
|
|  
|-
|
|
|
|
|
|
|
|
|
|
|}
 
==== Proof Theory ====
{| class="wikitable sortable"
! symbol
! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! eng-Latn-US: concept
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 概念
! jpn-Hrkt-JP: が↓いねん
! pes-Aran-IR: مَفهوم
! rus-Cyrl-RU: конце́пция
|-
|
|
|
|  
|
|
|
|
|
|
|-
| ⊢
|
|
|
| proof
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|}
 
==== Model Theory ====
{| class="wikitable sortable"
! symbol
! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! eng-Latn-US: concept
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 概念
! jpn-Hrkt-JP: が↓いねん
! pes-Aran-IR: مَفهوم
! rus-Cyrl-RU: конце́пция
|-
|
|
|
|
|
|
|
|
|
|  
|-
| ⊨
|
|
|
| model
|
|
|
|
|
|-
|
|  
|
|
|
|
|
|
|
|
|}
 
=== Process ===
{| class="wikitable sortable"
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn
! eng-Latn-US: process !! eng-Latn-US: constituent
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m]
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]
! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材
! jpn-Hrkt-JP: か↑てい !! jpn-Hrkt-JP: こ↑うざい
! pes-Aran-IR: فَرآیَند‎ !! pes-Aran-IR: هَمنِه
! rus-Cyrl-RU: проце́сс !! rus-Cyrl-RU: соста́вная часть
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
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|  ||
|  ||
|  ||
|  ||
|}
 
=== Resource under a Public License ===
{| class="wikitable sortable"
! name
! language
! link
|-
|
|
|
|-
|  
|
|
|}
 
<center>[[File:480px-Venn3tab.svg.png]]</center>
 
{{Sci-Tech-Index-Menu}}

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