Difference between revisions of "Language/Multiple-languages/Vocabulary/Mathematical-Logic"

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Line 2: Line 2:


{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 22: Line 22:
|  ||  
|  ||  
|-
|-
| set theory ||
| 集合论 ||  
| 集合论 ||  
| jíhé lùn ||  
| jíhé lùn ||  
| Mengenlehre [f] ||  
| Mengenlehre [f] ||  
| set theory ||
| théorie [f] des ensembles [m pl] ||  
| théorie [f] des ensembles [m pl] ||  
| 集合論 ||  
| 集合論 ||  
Line 32: Line 32:
| тео́рия мно́жеств ||  
| тео́рия мно́жеств ||  
|-
|-
| axiomatic set theory ||
| 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 [m pl] ||  
| théorie [f] axiomatique des ensembles [m pl] ||  
| 公理的集合論 ||  
| 公理的集合論 ||  
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| аксиомати́ческая тео́рия мно́жеств ||  
| аксиомати́ческая тео́рия мно́жеств ||  
|-
|-
| proof theory ||
| 证明论 ||  
| 证明论 ||  
| zhèngmíng lùn ||  
| zhèngmíng lùn ||  
| Beweistheorie [f] ||  
| Beweistheorie [f] ||  
| proof theory ||
| théorie [f] de la démonstration, théorie [f] de la preuve ||  
| théorie [f] de la démonstration, théorie [f] de la preuve ||  
| 証明論 ||  
| 証明論 ||  
Line 52: Line 52:
| тео́рия доказа́тельств ||  
| тео́рия доказа́тельств ||  
|-
|-
| model theory ||
| 模型论 ||  
| 模型论 ||  
| móxíng lùn ||  
| móxíng lùn ||  
| Modelltheorie [f] ||  
| Modelltheorie [f] ||  
| model theory ||
| théorie [f] des modèles [m pl] ||  
| théorie [f] des modèles [m pl] ||  
| モデル理論 ||  
| モデル理論 ||  
Line 62: Line 62:
| тео́рия моде́лей ||  
| тео́рия моде́лей ||  
|-
|-
| computability theory, recursion theory ||
| 可计算性理论 ||  
| 可计算性理论 ||  
| kějìsuànxìng lǐlùn ||  
| kějìsuànxìng lǐlùn ||  
| computability theory, recursion theory ||
| Berechenbarkeitstheorie [f], Rekursionstheorie [f] ||  
| Berechenbarkeitstheorie [f], Rekursionstheorie [f] ||  
| théorie [f] de la calculabilité ||  
| théorie [f] de la calculabilité ||  
Line 72: Line 72:
| тео́рия вычисли́мости ||  
| тео́рия вычисли́мости ||  
|-
|-
| type theory ||
| 类型论 ||  
| 类型论 ||  
| lèixíng lùn ||  
| lèixíng lùn ||  
| Typentheorie [f] ||  
| Typentheorie [f] ||  
| type theory ||
| théorie [f] des types [m pl] ||  
| théorie [f] des types [m pl] ||  
| 型理論 ||  
| 型理論 ||  
Line 82: Line 82:
| тео́рией ти́пов ||  
| тео́рией ти́пов ||  
|-
|-
| algebraic logic ||
| 代数逻辑 ||  
| 代数逻辑 ||  
| dàishù luóji ||  
| dàishù luóji ||  
| algebraische Logik ||  
| algebraische Logik ||  
| algebraic logic ||
| logique [f] algébrique ||  
| logique [f] algébrique ||  
|  ||  
|  ||  
Line 92: Line 92:
| алгебраи́ческая ло́гика ||  
| алгебраи́ческая ло́гика ||  
|-
|-
| Boolean algebra ||
| 逻辑代数，布尔代数 ||  
| 逻辑代数，布尔代数 ||  
| luóji dàishù, Bù'ěr dàishù ||  
| luóji dàishù, Bù'ěr dàishù ||  
| boolesche Algebra, boolescher Verband ||  
| boolesche Algebra, boolescher Verband ||  
| 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 ||  
Line 115: Line 115:
== Main ==
== Main ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 135: Line 135:
|  ||  
|  ||  
|-
|-
| function space || set; function
| 函数空间 ||  
| 函数空间 ||  
| hánshù kōngjiān ||  
| hánshù kōngjiān ||  
| Funktionenraum [m] ||  
| Funktionenraum [m] ||  
| function space || set; function
| espace fonctionnel ||  
| espace fonctionnel ||  
|  ||  
|  ||  
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| функциона́льное простра́нство ||  
| функциона́льное простра́нство ||  
|-
|-
| mathematical object ||
| 数学对象 ||  
| 数学对象 ||  
| shùxué duìxiàng ||  
| shùxué duìxiàng ||  
| mathematisches Objekt ||  
| mathematisches Objekt ||  
| mathematical object ||
| objet [m] mathématique ||  
| objet [m] mathématique ||  
|  ||  
|  ||  
Line 168: Line 168:
=== Set Theory ===
=== Set Theory ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 188: Line 188:
|  ||  
|  ||  
|-
|-
| argument || function
| 参数 ||  
| 参数 ||  
| cān shù ||  
| cān shù ||  
| Argument [m] ||  
| Argument [m] ||  
| argument || function
| argument [m] ||  
| argument [m] ||  
| 引数 ||  
| 引数 ||  
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| аксиомати́ческая тео́рия мно́жеств ||  
| аксиомати́ческая тео́рия мно́жеств ||  
|-
|-
| bijection, bijective function, one-to-one correspondence, or invertible function || function; set
| 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 ||  
Line 208: Line 208:
| бие́кция ||  
| бие́кция ||  
|-
|-
| binary operation, dyadic operation || operation
| 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 ||  
|-
|-
| cardinality || set
| 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 ||  
|-
|-
| cardinal number, cardinal || cardinality
| 基数 ||  
| 基数 ||  
| jī shù ||  
| jī shù ||  
| Kardinalzahl [f] ||  
| Kardinalzahl [f] ||  
| cardinal number, cardinal || cardinality
| nombre cardinal, cardinal [m] ||  
| nombre cardinal, cardinal [m] ||  
| 基数 ||  
| 基数 ||  
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| кардина́льное число́ ||  
| кардина́льное число́ ||  
|-
|-
| Cartesian product || ordered pair
| 笛卡尔积 ||  
| 笛卡尔积 ||  
| Díkǎ'ěr jī ||  
| Díkǎ'ěr jī ||  
| kartesisches Produkt, Mengenprodukt [n] ||  
| kartesisches Produkt, Mengenprodukt [n] ||  
| Cartesian product || ordered pair
| produit cartésien ||  
| produit cartésien ||  
| 直積，デカルト積 ||  
| 直積，デカルト積 ||  
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| прямо́е произведе́ние, дека́ртово произведе́ние ||  
| прямо́е произведе́ние, дека́ртово произведе́ние ||  
|-
|-
| choice function || function; empty set; direct product <algebra>
| 选择函数 ||  
| 选择函数 ||  
| xuǎnzé hánshù ||  
| xuǎnzé hánshù ||  
| Auswahlfunktion [f] ||  
| Auswahlfunktion [f] ||  
| choice function || function; empty set; direct product <algebra>
| fonction [f] de choix [m] ||  
| fonction [f] de choix [m] ||  
| 選択関数 ||  
| 選択関数 ||  
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| фу́нкция вы́бора ||  
| фу́нкция вы́бора ||  
|-
|-
| class || set
| 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 ||  
|-
|-
| codomain, set of destination || function
| 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 ||  
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| о́бласть значе́ний ||  
| о́бласть значе́ний ||  
|-
|-
| continuum || cardinal number
| 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 ||  
|-
|-
| domain, set of departure || function
| 定义域 ||  
| 定义域 ||  
| dìngyì yù ||  
| dìngyì yù ||  
| Definitionsmenge [f], Definitionsbereich [m] ||  
| Definitionsmenge [f], Definitionsbereich [m] ||  
| domain, set of departure || function
| ensemble [m] de définition [f] ||  
| ensemble [m] de définition [f] ||  
| 定義域 ||  
| 定義域 ||  
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| о́бласть определе́ния ||  
| о́бласть определе́ния ||  
|-
|-
| element || mathematical object
| 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 ||  
|-
|-
| enumeration || set
| 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 ||  
|-
|-
| equality ||
| 相等 ||  
| 相等 ||  
| xiāng děng ||  
| xiāng děng ||  
| Gleichheit [f] ||  
| Gleichheit [f] ||  
| equality ||
| égalité [f] ||  
| égalité [f] ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| expression || digit; symbol
| 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 ||  
| 数式 ||  
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| выраже́ние ||  
| выраже́ние ||  
|-
|-
| extensionality, c || mathematical object
| 外延性 ||  
| 外延性 ||  
| wàiyán xìng ||  
| wàiyán xìng ||  
| Extensionalität [f] ||  
| Extensionalität [f] ||  
| extensionality, extensional equality || mathematical object
|  ||  
|  ||  
| 外延性 ||  
| 外延性 ||  
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|  ||  
|  ||  
|-
|-
| identity element, neutral element || binary operation; set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| identity element, neutral element || binary operation; set
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| identity function, identity relation, identity map, identity transformation || argument
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| identity function, identity relation, identity map, identity transformation || argument
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| image || function; set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| image || function; set
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| indexed family, family || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| indexed family, family || set
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| inequality || equality
| 不等 ||  
| 不等 ||  
| bù děng ||  
| bù děng ||  
| Ungleichheit [f] ||  
| Ungleichheit [f] ||  
| inequality || equality
| inégalité [f] ||  
| inégalité [f] ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| injection, injective function, one-to-one function || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| injection, injective function, one-to-one function || function
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| inverse image, preimage || codomain; subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| inverse image, preimage || codomain; subset
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| mapping || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| mapping || function
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| operand || operation
| 运算数，运算元 ||  
| 运算数，运算元 ||  
| yùnsuàn shù, yùnsuàn yuán ||  
| yùnsuàn shù, yùnsuàn yuán ||  
| Operand [m] ||  
| Operand [m] ||  
| operand || operation
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| operation ||
| 运算 ||  
| 运算 ||  
| yùnsuàn ||  
| yùnsuàn ||  
| Verknüpfung [f] ||  
| Verknüpfung [f] ||  
| operation ||
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| ordinal number || enumeration; ordinal numeral <linguistics>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| ordinal number || enumeration; ordinal numeral <linguistics>
|  ||  
|  ||  
|  ||  
|  ||  
Line 458: Line 458:
|  ||  
|  ||  
|-
|-
| range || codomain; image
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| range || codomain; image
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| relation || set
| 关系 ||  
| 关系 ||  
| guānxi ||  
| guānxi ||  
| Relation [f] ||  
| Relation [f] ||  
| relation || set
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| Russell's paradox, Russell's antinomy || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Russell's paradox, Russell's antinomy || set
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| set || element
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| set || element
|  ||  
|  ||  
|  ||  
|  ||  
Line 498: Line 498:
|  ||  
|  ||  
|-
|-
| surjection, surjective function, onto function || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| surjection, surjective function, onto function || function
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| symmetric difference, disjunctive union || intersection
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| symmetric difference, disjunctive union || intersection
|  ||  
|  ||  
|  ||  
|  ||  
Line 518: Line 518:
|  ||  
|  ||  
|-
|-
| tree || partially ordered set; well-ordered set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| tree || partially ordered set; well-ordered set
|  ||  
|  ||  
|  ||  
|  ||  
Line 528: Line 528:
|  ||  
|  ||  
|-
|-
| tuple || element; sequence <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| tuple || element; sequence <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 538: Line 538:
|  ||  
|  ||  
|-
|-
| universe ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| universe ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 548: Line 548:
|  ||  
|  ||  
|-
|-
| urelement || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| urelement || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 558: Line 558:
|  ||  
|  ||  
|-
|-
| Venn diagram || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Venn diagram || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 581: Line 581:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ property of binary operation
|+ property of binary operation
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 591: Line 591:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| property of binary operation ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| property of binary operation ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 611: Line 611:
|  ||  
|  ||  
|-
|-
| anticommutative property, anticommutativity || operation
| 反交换律 ||  
| 反交换律 ||  
| fǎnjiāohuàn lǜ ||  
| fǎnjiāohuàn lǜ ||  
| Antikommutativgesetz [n], Antikommutativität [f] ||  
| Antikommutativgesetz [n], Antikommutativität [f] ||  
| anticommutative property, anticommutativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
Line 621: Line 621:
|  ||  
|  ||  
|-
|-
| associative property, associativity || operation
| 结合律 ||  
| 结合律 ||  
| jiéhé lǜ ||  
| jiéhé lǜ ||  
| Assoziativgesetz [n], Assoziativität [f] ||  
| Assoziativgesetz [n], Assoziativität [f] ||  
| associative property, associativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
Line 631: Line 631:
|  ||  
|  ||  
|-
|-
| commutative property, commutativity || operation
| 交换律 ||  
| 交换律 ||  
| jiāohuàn lǜ ||  
| jiāohuàn lǜ ||  
| Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f] ||  
| Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f] ||  
| commutative property, commutativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
Line 641: Line 641:
|  ||  
|  ||  
|-
|-
| distributive property, distributivity || operation
| 分配律 ||  
| 分配律 ||  
| fēnpèi lǜ ||  
| fēnpèi lǜ ||  
| Distributivgesetz [n], Distributivität [f] ||  
| Distributivgesetz [n], Distributivität [f] ||  
| distributive property, distributivity || operation
|  ||  
|  ||  
|  ||  
|  ||  
Line 664: Line 664:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ operation on set
|+ operation on set
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 674: Line 674:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| operation on set ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| operation on set ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 694: Line 694:
|  ||  
|  ||  
|-
|-
| absolute complement || complement; subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| absolute complement || complement; subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 704: Line 704:
|  ||  
|  ||  
|-
|-
| complement. set difference || set
| 补集 ||  
| 补集 ||  
| bǔ jí ||  
| bǔ jí ||  
| Komplement [n] ||  
| Komplement [n] ||  
| complement, set difference || set
| complémentaire [m] ||  
| complémentaire [m] ||  
| 差集合 ||  
| 差集合 ||  
Line 714: Line 714:
| ра́зность мно́жеств ||  
| ра́зность мно́жеств ||  
|-
|-
| intersection || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| intersection || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 724: Line 724:
|  ||  
|  ||  
|-
|-
| power set, powerset || subset; empty set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| power set, powerset || subset; empty set
|  ||  
|  ||  
|  ||  
|  ||  
Line 734: Line 734:
|  ||  
|  ||  
|-
|-
| relative complement || complement; subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| relative complement || complement; subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 744: Line 744:
|  ||  
|  ||  
|-
|-
| union || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| union || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 767: Line 767:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ system of set theory
|+ system of set theory
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 777: Line 777:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| system of set theory ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| system of set theory ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 810: Line 800:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
| Zermelo–Fraenkel set theory || axiomatic system
| Zermelo–Fraenkel set theory || axiomatic system
|  ||
|  ||
|  ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 840: Line 820:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ type of set
|+ type of set
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 850: Line 830:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| type of set ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| type of set ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 870: Line 850:
|  ||  
|  ||  
|-
|-
| countable set || subset; cardinality
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| countable set || subset; cardinality
|  ||  
|  ||  
|  ||  
|  ||  
Line 880: Line 860:
|  ||  
|  ||  
|-
|-
| empty set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| empty set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 890: Line 870:
|  ||  
|  ||  
|-
|-
| finite set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| finite set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 900: Line 880:
|  ||  
|  ||  
|-
|-
| fuzzy set, uncertain set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| fuzzy set, uncertain set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 910: Line 890:
|  ||  
|  ||  
|-
|-
| infinite set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| infinite set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 920: Line 900:
|  ||  
|  ||  
|-
|-
| proper subset || subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| proper subset || subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 930: Line 910:
|  ||  
|  ||  
|-
|-
| singleton. unit set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| singleton. unit set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 940: Line 920:
|  ||  
|  ||  
|-
|-
| subset || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| subset || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 950: Line 930:
|  ||  
|  ||  
|-
|-
| superset || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| superset || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 960: Line 940:
|  ||  
|  ||  
|-
|-
| transitive set || subset; urelement
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| transitive set || subset; urelement
|  ||  
|  ||  
|  ||  
|  ||  
Line 970: Line 950:
|  ||  
|  ||  
|-
|-
| universal set || mathematical object
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| universal set || mathematical object
|  ||  
|  ||  
|  ||  
|  ||  
Line 980: Line 960:
|  ||  
|  ||  
|-
|-
| unordered pair, pair set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| unordered pair, pair set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 990: Line 970:
|  ||  
|  ||  
|-
|-
| well-founded set || transitive closure
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-founded set || transitive closure
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,000: Line 980:
|  ||  
|  ||  
|-
|-
| well-ordered set || well-order; total order; non-empty set; least element
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-ordered set || well-order; total order; non-empty set; least element
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,023: Line 1,003:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ binary relation
|+ binary relation
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,033: Line 1,013:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| binary relation || relation
| 二元关系 ||  
| 二元关系 ||  
| èryuán guānxi ||  
| èryuán guānxi ||  
| binäre Relation ||  
| binäre Relation ||  
| binary relation || relation
| relation [f] binaire ||  
| relation [f] binaire ||  
|  ||  
|  ||  
Line 1,053: Line 1,033:
|  ||  
|  ||  
|-
|-
| connected relation, total relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| connected relation, total relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,063: Line 1,043:
|  ||  
|  ||  
|-
|-
| converse relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| converse relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,073: Line 1,053:
|  ||  
|  ||  
|-
|-
| equivalence relation || reflexive relation; symmetric relation; transitive relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| equivalence relation || reflexive relation; symmetric relation; transitive relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,083: Line 1,063:
|  ||  
|  ||  
|-
|-
| finitary relation || Cartesian product
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| finitary relation || Cartesian product
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,093: Line 1,073:
|  ||  
|  ||  
|-
|-
| symmetric relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| symmetric relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,103: Line 1,083:
|  ||  
|  ||  
|-
|-
| transitive relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| transitive relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,113: Line 1,093:
|  ||  
|  ||  
|-
|-
| well-founded relation || class; minimal element; empty set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-founded relation || class; minimal element; empty set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,123: Line 1,103:
|  ||  
|  ||  
|-
|-
| well-order, well-order relation, well-ordering ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-order, well-order relation, well-ordering ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,146: Line 1,126:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ function
|+ function
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,156: Line 1,136:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| function || binary relation; set
| 函数 ||  
| 函数 ||  
| hán shù ||  
| hán shù ||  
| Funktion [f] ||  
| Funktion [f] ||  
| function || binary relation; set
| fonction [f] ||  
| fonction [f] ||  
|  ||  
|  ||  
Line 1,176: Line 1,156:
|  ||  
|  ||  
|-
|-
| Boolean function || argument; Boolean domain <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Boolean function || argument; Boolean domain <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,186: Line 1,166:
|  ||  
|  ||  
|-
|-
| Boolean-valued function || function; value; Boolean domain <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Boolean-valued function || function; value; Boolean domain <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,196: Line 1,176:
|  ||  
|  ||  
|-
|-
| complex-valued function || function; value; complex number
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| complex-valued function || function; value; complex number
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,206: Line 1,186:
|  ||  
|  ||  
|-
|-
| functions of several complex variables || argument; complex variable
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| functions of several complex variables || argument; complex variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,216: Line 1,196:
|  ||  
|  ||  
|-
|-
| function of several real variables, real multivariate function || argument; real variable
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| function of several real variables, real multivariate function || argument; real variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,226: Line 1,206:
|  ||  
|  ||  
|-
|-
| integer-valued function || function; value; integer
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integer-valued function || function; value; integer
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,236: Line 1,216:
|  ||  
|  ||  
|-
|-
| ordered pair || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| ordered pair || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,246: Line 1,226:
|  ||  
|  ||  
|-
|-
| real-valued function || function; value; real number
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| real-valued function || function; value; real number
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,269: Line 1,249:
==== Axiomatic Set Theory ====
==== Axiomatic Set Theory ====
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,289: Line 1,269:
|  ||  
|  ||  
|-
|-
| amorphous set || infinite set; disjoint union; subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| amorphous set || infinite set; disjoint union; subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,299: Line 1,279:
|  ||  
|  ||  
|-
|-
| normal function || ordinal number; monotonically increasing function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| normal function || ordinal number; monotonically increasing function
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,322: Line 1,302:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ axiom of choice
|+ axiom of choice
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,332: Line 1,312:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| axiom of choice || choice function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| axiom of choice || choice function
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,365: Line 1,345:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ theorem in set theory
|+ theorem in set theory
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,375: Line 1,355:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| theorem in set theory ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| theorem in set theory ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,395: Line 1,375:
|  ||  
|  ||  
|-
|-
| Cantor's theorem || power set; cardinality
| 康托尔定理 ||  
| 康托尔定理 ||  
| Kāngtuō'ěr dìnglǐ ||  
| Kāngtuō'ěr dìnglǐ ||  
| Satz [m] von Cantor ||  
| Satz [m] von Cantor ||  
| Cantor's theorem || power set; cardinality
| théorème [m] de Cantor ||  
| théorème [m] de Cantor ||  
| カントールの定理 ||  
| カントールの定理 ||  
Line 1,405: Line 1,385:
| теоре́ма Ка́нтора ||  
| теоре́ма Ка́нтора ||  
|-
|-
| well-ordering theorem, Zermelo's theorem || well-order
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-ordering theorem, Zermelo's theorem || well-order
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,428: Line 1,408:
=== Proof Theory ===
=== Proof Theory ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,448: Line 1,428:
|  ||  
|  ||  
|-
|-
| mathematical induction ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| mathematical induction ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,458: Line 1,438:
|  ||  
|  ||  
|-
|-
| sequent ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| sequent ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,471: Line 1,451:
=== Model Theory ===
=== Model Theory ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,491: Line 1,471:
|  ||  
|  ||  
|-
|-
| elementary equivalence || structure; signature
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| elementary equivalence || structure; signature
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,501: Line 1,481:
|  ||  
|  ||  
|-
|-
| signature || non-logical symbol <logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| signature || non-logical symbol <logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,511: Line 1,491:
|  ||  
|  ||  
|-
|-
| structure || cardinality; arity
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| structure || cardinality; arity
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,534: Line 1,514:
=== Computability Theory ===
=== Computability Theory ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,567: Line 1,547:
=== Type Theory ===
=== Type Theory ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,587: Line 1,567:
|  ||  
|  ||  
|-
|-
| boolean type || type
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| boolean type || type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,597: Line 1,577:
|  ||  
|  ||  
|-
|-
| bottom type || type
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| bottom type || type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,607: Line 1,587:
|  ||  
|  ||  
|-
|-
| identity type, propositional equality || equality; type
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| identity type, propositional equality || equality; type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,617: Line 1,597:
|  ||  
|  ||  
|-
|-
| product type || type
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| product type || type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,627: Line 1,607:
|  ||  
|  ||  
|-
|-
| unit type || type
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| unit type || type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,650: Line 1,630:
=== Algebraic Logic ===
=== Algebraic Logic ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,671: Line 1,651:
==== Boolean Algebra ====
==== Boolean Algebra ====
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,689: Line 1,669:
|  ||  
|  ||  
|-
|-
| De Morgan's laws || conjunction; disjunction; negation
| 德摩根定律 ||  
| 德摩根定律 ||  
| Dé Mógēn dìnglǜ ||  
| Dé Mógēn dìnglǜ ||  
| De-Morgansche Gesetze [n pl], De-Morgansche Regeln [f pl] ||  
| De-Morgansche Gesetze [n pl], De-Morgansche Regeln [f pl] ||  
| De Morgan's laws || conjunction; disjunction; negation
| lois [f pl] de De Morgan ||  
| lois [f pl] de De Morgan ||  
| ド・モルガンの法則 ||  
| ド・モルガンの法則 ||  
Line 1,698: Line 1,678:
| зако́ны де Мо́ргана, пра́вила де Мо́ргана ||  
| зако́ны де Мо́ргана, пра́вила де Мо́ргана ||  
|-
|-
| truth table || expression
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| truth table || expression
| table [f] de vérité ||  
| table [f] de vérité ||  
|  ||  
|  ||  
Line 1,720: Line 1,700:
=== Sentence ===
=== Sentence ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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 1,755: Line 1,735:
{| class="wikitable sortable"
{| class="wikitable sortable"
! symbol
! symbol
! eng-Latn-US: concept
! cmn-Hans-CN: 概念
! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! deu-Latn-DE: Begriff [m]
! eng-Latn-US: concept
! fra-Latn-FR: concept [m]
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 概念
! jpn-Jpan-JP: 概念
Line 1,777: Line 1,757:
|-
|-
| =
| =
| is equal to
|  
|  
|  
|  
|  
|  
| is equal to
|  
|  
|  
|  
Line 1,788: Line 1,768:
|-
|-
| ≠
| ≠
| is not equal to
|  
|  
|  
|  
|  
|  
| is not equal to
|  
|  
|  
|  
Line 1,799: Line 1,779:
|-
|-
| ∈
| ∈
| is element of
|  
|  
|  
|  
|  
|  
| is element of
|  
|  
|  
|  
Line 1,810: Line 1,790:
|-
|-
| ∉
| ∉
| is not element of
|  
|  
|  
|  
|  
|  
| is not element of
|  
|  
|  
|  
Line 1,821: Line 1,801:
|-
|-
| ∋
| ∋
| contains member
|  
|  
|  
|  
|  
|  
| contains member
|  
|  
|  
|  
Line 1,832: Line 1,812:
|-
|-
| ∌
| ∌
| does not contain member
|  
|  
|  
|  
|  
|  
| does not contain member
|  
|  
|  
|  
Line 1,843: Line 1,823:
|-
|-
| ⊂
| ⊂
| is subset of; is proper subset of
|  
|  
|  
|  
|  
|  
| is subset of; is proper subset of
|  
|  
|  
|  
Line 1,854: Line 1,834:
|-
|-
| ⊃
| ⊃
| is superset of; is proper superset of
|  
|  
|  
|  
|  
|  
| is superset of; is proper superset of
|  
|  
|  
|  
Line 1,865: Line 1,845:
|-
|-
| ⊆
| ⊆
| is subset of
|  
|  
|  
|  
|  
|  
| is subset of
|  
|  
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{| class="wikitable sortable"
{| class="wikitable sortable"
! symbol
! symbol
! eng-Latn-US: concept
! cmn-Hans-CN: 概念
! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! deu-Latn-DE: Begriff [m]
! eng-Latn-US: concept
! fra-Latn-FR: concept [m]
! fra-Latn-FR: concept [m]
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! jpn-Jpan-JP: 概念
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{| class="wikitable sortable"
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! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! deu-Latn-DE: Begriff [m]
! eng-Latn-US: concept
! fra-Latn-FR: concept [m]
! fra-Latn-FR: concept [m]
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=== Process ===
=== Process ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: process !! eng-Latn-US: constituent
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn
! 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]
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m]
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]

Revision as of 08:12, 26 March 2022

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On this page you will find a part of the Sci–Tech Index, a project for science and technology learners.

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
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 computability theory, recursion theory Berechenbarkeitstheorie [f], Rekursionstheorie [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 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

Main

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

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
参数 cān shù Argument [m] argument function argument [m] 引数 ひ↑きす↓う аксиомати́ческая тео́рия мно́жеств
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 о́бласть значе́ний
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] تَساوی
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 外延性 が↑いえんせい
identity element, neutral element binary operation; set
identity function, identity relation, identity map, identity transformation argument
image function; set
indexed family, family set
不等 bù děng Ungleichheit [f] inequality equality inégalité [f]
injection, injective function, one-to-one function function
inverse image, preimage codomain; subset
mapping function
运算数，运算元 yùnsuàn shù, yùnsuàn yuán Operand [m] operand operation
运算 yùnsuàn Verknüpfung [f] operation
ordinal number enumeration; ordinal numeral <linguistics>
range codomain; image
关系 guānxi Relation [f] relation set
Russell's paradox, Russell's antinomy set
set element
surjection, surjective function, onto function function
symmetric difference, disjunctive union intersection
tree partially ordered set; well-ordered set
tuple element; sequence <number theory>
universe
urelement set
Venn diagram set
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
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
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
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
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
Zermelo–Fraenkel set theory axiomatic system
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
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
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
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
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]
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

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
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
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
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

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
mathematical induction
sequent

Model 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
elementary equivalence structure; signature
signature non-logical symbol <logic>
structure cardinality; arity

Computability 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

Type 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
boolean type type
bottom type type
identity type, propositional equality equality; type
product type type
unit type type

Algebraic Logic

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

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

Appendix

Sentence

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

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

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

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

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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Sci–Tech Index

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Philosophy

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