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{{Sci-Tech-Index-Intro}}
[[Category:Sci–Tech_Index]]
This is a part of the [https://polyglotclub.com/wiki/Language/Multiple-languages/Culture/Introduction-to-Sci%E2%80%93Tech-Index Sci–Tech Index], a project for science and technology learners.


{| class="wikitable sortable"
In progress.
! cmn-Hans-CN: 科目
! cmn-Latn.Pinyin-CN: kēmù
! deu-Latn-DE: Fach [n]
! eng-Latn-US: subject
! fra-Latn-FR: matière [f]
! jpn-Jpan-JP: 科目
! jpn-Hrkt-JP: か↑もく
! pes-Aran-IR: رِشته
! rus-Cyrl-RU: предме́т
|-
|
|
|
|
|
|
|
|
|
|-
| 集合论
| jíhé lùn
| Mengenlehre [f]
| set theory
| théorie [f] des ensembles [m pl]
| 集合論
| しゅ↑うご↓うろん
|
| тео́рия мно́жеств
|-
| 公理化集合论
| gǒnglǐhuà jíhélùn
| axiomatische Mengenlehre
| axiomatic set theory
| théorie [f] axiomatique des ensembles [m pl]
| 公理的集合論
| こ↑うりてき↓しゅ↑うご↓うろん
|
| аксиомати́ческая тео́рия мно́жеств
|-
| 证明论
| zhèngmíng lùn
| Beweistheorie [f]
| proof theory
| théorie [f] de la démonstration, théorie [f] de la preuve
| 証明論
| しょ↑うめ↓いろん
|
| тео́рия доказа́тельств
|-
| 模型论
| móxíng lùn
| Modelltheorie [f]
| model theory
| théorie [f] des modèles [m pl]
| モデル理論
| モ↑デルり↓ろん
|
| тео́рия моде́лей
|-
| 可计算性理论
| kějìsuànxìng lǐlùn
| Berechenbarkeitstheorie [f], Rekursionstheorie [f]
| computability theory, recursion theory
| théorie [f] de la calculabilité
| 計算可能性理論
| け↑いさんかのうせいり↓ろん
|
| тео́рия вычисли́мости
|-
| 类型论
| lèixíng lùn
| Typentheorie [f]
| type theory
| théorie [f] des types [m pl]
| 型理論
| か↑たり↓ろん
|
| тео́рией ти́пов
|-
| 代数逻辑
| dàishù luóji
| algebraische Logik
| algebraic logic
| logique [f] algébrique
|
|
|
| алгебраи́ческая ло́гика
|-
| 逻辑代数，布尔代数
| luóji dàishù, Bù'ěr dàishù
| boolesche Algebra, boolescher Verband
| Boolean algebra
| algèbre [f] de Boole, algèbre booléenne
| ブール代数，ブール束
| ブ↑ールだ↓いすう，ブ↑ールそく
|
| а́лгебра ло́гики, а́лгебра выска́зываний
|-
|
|
|
|
|
|
|
|
|
|}


{| 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 134: Line 25:
|  ||  
|  ||  
|-
|-
| 函数空间 ||  
| set theory ||  
| hánshù kōngjiān ||  
| 集合论 ||  
| Funktionenraum [m] ||  
| jíhé lùn ||
| function space || set; function
| Mengenlehre [f] ||  
| espace fonctionnel ||  
| théorie [f] des ensembles ||
| 集合論 ||
| しゅ↑うご↓うろん ||
| ||  
| тео́рия мно́жеств ||
|-
| axiomatic set theory ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
| proof theory ||
| 证明论 ||
| zhèngmíng lùn ||
| Beweistheorie [f] ||
| théorie [f] de la démonstration, théorie [f] de la preuve ||
| 証明論 ||
| しょ↑うめ↓いろん ||
|  ||
| тео́рия доказа́тельств ||
|-
| model theory ||
| 模型论 ||
| móxíng lùn ||
| Modelltheorie [f] ||
| théorie [f] des modèles ||
| モデル理論 ||
| モ↑デルり↓ろん ||  
|  ||  
|  ||  
| 関数空間 ||
| тео́рия моде́лей ||  
| か↑んすうく↓うかん ||
| функциона́льное простра́нство ||  
|-
|-
| 数学对象 ||  
| computability theory, recursion theory ||  
| shùxué duìxiàng ||  
| 可计算性理论 ||  
| mathematisches Objekt ||  
| kějìsuànxìng lǐlùn ||  
| mathematical object ||  
| Berechenbarkeitstheorie [f], Rekursionstheorie [f] ||  
| objet [m] mathématique ||  
| théorie [f] de la calculabilité ||
| 計算可能性理論 ||
| け↑いさんかのうせいり↓ろん ||  
|  ||  
|  ||  
| 数学的対象 ||
| тео́рия вычисли́мости ||  
| す↑うがくてきた↓いしょう ||
| математи́ческий объе́кт ||  
|-
|-
|  ||  
|  ||  
Line 167: Line 88:
== 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 187: Line 108:
|  ||  
|  ||  
|-
|-
| 参数 ||  
| amorphous set || infinite set; disjoint union; subset
| cān shù ||  
| ||  
| Argument [m] ||
| ||  
| argument || function
| argument [m] ||
| 引数 ||
| ひ↑きす↓う ||  
|  ||  
|  ||  
| аргуме́нт ||
|-
| 双射 ||
| shuāng shè ||
| Bijektion [f], bijektive Funktion ||
| bijection, bijective function, invertible function || function; set
| bijection [f] ||
| 全単射，双射 ||
| ぜ↑んた↓んしゃ，そ↓うしゃ ||
|  ||  
|  ||  
| бие́кция ||
|-
| 二元运算 ||
| èryuán yùnsuàn ||
| zweistellige Verknüpfung, binäre Verknüpfung ||
| binary operation, dyadic operation || operation
| opération [f] binaire ||
| 二項演算 ||
| に↑こうえ↓んざん ||
|  ||  
|  ||  
| бина́рная опера́ция, двуме́стная опера́ция ||
|-
| 势，浓度 ||
| shì, nóng dù ||
| Mächtigkeit [f], Kardinalität [f] ||
| cardinality || set
| cardinalité [f] ||
| 濃度，カーディナリティ ||
| の↓うど，カ↑ーディナ↓リティ ||
|  ||  
|  ||  
| мо́щность ||
|-
| 基数 ||
| jī shù ||
| Kardinalzahl [f] ||
| cardinal number, cardinal || cardinality
| nombre cardinal, cardinal [m] ||
| 基数 ||
| き↑す↓う ||
|  ||  
|  ||  
| кардина́льное число́ ||
|-
| 笛卡尔积 ||
| Díkǎ'ěr jī ||
| kartesisches Produkt, Mengenprodukt [n] ||
| Cartesian product || ordered pair
| produit cartésien ||
| 直積，デカルト積 ||
| ちょ↑くせ↓き，デ↑カルト­せ↓き ||
|  ||  
|  ||  
| прямо́е произведе́ние, дека́ртово произведе́ние ||
|-
|-
| 选择函数 ||  
| anticommutative property, anticommutativity || operation
| xuǎnzé hánshù ||  
| 反交换律 ||  
| Auswahlfunktion [f] ||  
| fǎnjiāohuàn lǜ ||  
| choice function || function; empty set; direct product <algebra>
| Antikommutativgesetz [n], Antikommutativität [f] ||  
| fonction [f] de choix [m] ||
| 選択関数 ||
| せ↑んたくか↓んすう ||  
|  ||  
|  ||  
| фу́нкция вы́бора ||
|-
| 类 ||
| lèi ||
| Klasse [f] ||
| class || set
| classe [f] ||
| クラス，類 ||
| ク↓ラス，る↓い ||
|  ||  
|  ||  
| класс ||
|-
| 到达域，陪域，上域，终域 ||
| dàodá yù, péi yù, shàng yù, zhōng yù ||
| Zielmenge [f], Wertevorrat [m] ||
| codomain, set of destination || function
| ensemble [m] d'arrivée [f] ||
| 終域 ||
| し↑ゅうい↓き ||
|  ||  
|  ||  
|  ||  
|  ||  
|-
| 连续统 ||
| liánxù tǒng ||
| Kontinuum [m] ||
| continuum || cardinal number
| continu [m] ||
| 連続体 ||
| れ↑んぞくたい ||
|  ||  
|  ||  
| конти́нуум ||
|-
|-
| 定义域 ||
| argument || function
| dìngyì yù ||
| Definitionsmenge [f], Definitionsbereich [m] ||
| domain, set of departure || function
| ensemble [m] de définition [f] ||
| 定義域 ||
| て↑いぎ↓いき ||
|  ||  
|  ||  
| о́бласть определе́ния ||
|-
| 元素 ||
| yuánsù ||
| Element [n] ||
| element || mathematical object
| élément [m] ||
| 元 ||
| げ↓ん ||
|  ||  
|  ||  
| элеме́нт ||
|-
| 列举法 ||
| lièjǔ fǎ ||
| Aufzählung [f] ||
| enumeration || set
| énumération [f] ||
| 数え上げ ||
| か↑ぞえあげ ||
|  ||  
|  ||  
| перечисле́ние ||
|-
| 相等 ||
| xiāng děng ||
| Gleichheit [f] ||
| equality ||
| égalité [f] ||
| 相等 ||
| そ↑うとう ||
| تَساوی ||
| ра́венство ||
|-
| 表达式，表示式，运算式 ||
| biǎodá shì, biǎoshì shì, yùnsuàn shì ||
| Ausdruck [m] ||
| expression || digit; symbol
| expression [f] ||
| 数式 ||
| す↑うしき ||
|  ||  
|  ||  
| выраже́ние ||
|-
| 外延性 ||
| wàiyán xìng ||
| Extensionalität [f] ||
| extensionality, extensional equality || mathematical object
| extensionnalité [f] ||
| 外延性 ||
| が↑いえんせい ||
|  ||  
|  ||  
| экстенсиона́льность [ж] ||
|-
| 单位元 ||
| dānwèi yuán ||
| neutrales Element ||
| identity element, neutral element || binary operation; set
| élément [m] neutre, élément [m] identité ||
| 単位元，中立元 ||
| た↑んいげ↓ん，ちゅ↑うりつげ↓ん ||
|  ||  
|  ||  
| нейтра́льный элеме́нт ||
|-
| 恒等函数 ||
| héngděng hánshù ||
| identische Abbildung ||
| identity function, identity relation, identity map, identity transformation || argument
| application [f] identité, fonction [f] identité ||
| 恒等写像 ||
| こ↑うとうしゃ↓ぞう ||
|  ||  
|  ||  
| тожде́ственное отображе́ние ||
|-
| 像 ||
| xiàng ||
| Bild [n], Bildbereich [m], Bildmenge [f] ||
| image || function
| image [f] ||
| 像 ||
| ぞ↓う ||
|  ||  
|  ||  
| о́браз ||
|-
|-
| 族 ||  
| associative property, associativity || operation
| zú ||  
| 结合律 ||  
| Familie [f] ||  
| jiéhé lǜ ||  
| indexed family, family || set
| Assoziativgesetz [n], Assoziativität [f] ||  
| famille ||
| 族 ||
| ぞ↑く ||  
|  ||  
|  ||  
| семе́йство, индекси́рованное семе́йство ||
|-
| 不等 ||
| bù děng ||
| Ungleichheit [f] ||
| inequality || equality
| inégalité [f] ||
| 不等 ||
| ふ↑とう ||
|  ||  
|  ||  
| нера́венство ||
|-
| 单射 ||
| dān shè ||
| injektive Funktion ||
| injection, injective function, one-to-one function || function; injectivity
| injection [f] ||
| 単射 ||
| た↑んしゃ ||
|  ||  
|  ||  
| инъе́кция, инъекти́вное отображе́ние ||
|-
| 原像 ||
| yuán xiàng ||
| Urbild [n] ||
| inverse image, preimage || codomain; subset
| image [f] réciproque, préimage [f] ||
| 逆像，原像 ||
| ぎゃ↑くぞう，げ↑んぞう ||
|  ||  
|  ||  
| обра́тный о́браз, проо́браз ||
|-
| 映射 ||
| yìngshè ||
| Abbildung [f] ||
| mapping || function
| application [f] ||
| 写像 ||
| しゃ↑ぞう ||
|  ||  
|  ||  
| отображе́ние ||
|-
|-
| 运算数，运算元 ||
| bijection, bijective function, one-to-one correspondence, or invertible function || function; set
| yùnsuàn shù, yùnsuàn yuán ||
| Operand [m] ||
| operand || operation
| opérande [m] ||
| 被演算子 ||
| ひ↑えんざ↓んし ||  
|  ||  
|  ||  
| опера́нд  ||
|-
| 运算 ||
| yùnsuàn ||
| Verknüpfung [f] ||
| operation ||
| opération [f] ||
| 演算 ||
| え↑んざん ||
|  ||  
|  ||  
| oпера́ция ||
|-
| 序数 ||
| xù shù ||
| Ordinalzahl [f] ||
| ordinal number || enumeration; ordinal numeral <linguistics>
| nombre ordinal ||
| 順序数 ||
| じゅ↑んじょ↓すう ||
|  ||  
|  ||  
| поря́дковым число́м, ордина́лом ||
|-
| 值域 ||
| zhí yù ||
| Bild [n] (Funktion), Bildbereich [m] (Funktion), Bildmenge [f] (Funktion) ||
| range || image
| image [f] (application) ||
| 値域 ||
| ち↓いき ||
|  ||  
|  ||  
| о́бласть значе́ний фу́нкции, мно́жество значе́ний фу́нкции ||
|-
| 关系 ||
| guānxi ||
| Relation [f] ||
| relation || set
| relation [f] ||
| 関係 ||
| かんけい ||
|  ||  
|  ||  
| отноше́ние ||
|-
| 罗素悖论 ||
| Luósù bèilùn ||
| Russellsche Antinomie ||
| Russell's paradox, Russell's antinomy || set
| paradoxe [m] de Russell, antinomie [f] de Russell ||
| ラッセルのパラドックス ||
| ラ↓ッセルのパ↑ラド↓ックス ||
|  ||  
|  ||  
| парадо́кс Ра́ссела, антино́мия Ра́ссела ||
|-
| 集合，集 ||
| jíhé, jí ||
| Menge [f] ||
| set || element
| ensemble [m] ||
| 集合 ||
| しゅ↑うごう ||
|  ||  
|  ||  
| мно́жество ||
|-
| 满射 ||
| mǎn shè ||
| surjektive Funktion ||
| surjection, surjective function, onto function || function
| surjection [f], application surjective ||
| 全射 ||
| ぜ↑んしゃ ||
|  ||  
|  ||  
| сюръе́кция, сюръекти́вное отображе́ние ||
|-
|-
| 对称差 ||
| axiom of choice || choice function
| duìchèn chā ||
| symmetrische Differenz ||
| symmetric difference, disjunctive union || intersection
| différence [f] symétrique ||
| 対称差 ||
| た↑いしょうさ ||  
|  ||  
|  ||  
| симметри́ческая ра́зность ||
|-
| 多元组 ||
| duōyuán zǔ ||
| Tupel [n] ||
| tuple || element; sequence <number theory>
| uplet [m] ||
| 順序組，組 ||
| じゅ↑んじょぐみ，く↑み ||
|  ||  
|  ||  
| корте́ж ||
|-
| 全集 ||
| quán jí ||
| Universalmenge [f], Allmenge [f], Grundmenge [f] ||
| universal set || universe
| ensemble référentiel ||
| 全体集合，普遍集合 ||
| ぜ↑んたいしゅ↓うごう，ふ↑へんしゅ↓うごう ||
|  ||  
|  ||  
| универса́льное мно́жество ||
|-
| 全类 ||
| quán lèi ||
| Universum [n] ||
| universe || class
| univers [m] ||
| 宇宙 ||
| う↓ちゅう ||
|  ||  
|  ||  
| универса́льный класс ||
|-
| 基本元素 ||
| jīběn yuánsù ||
| Urelement [n] ||
| urelement || set
| ur-element [m] ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| урэлеме́нт ||
|-
| 范恩图，维恩图，韦恩图，文氏图 ||
| Fàn'ēn tú, Wéi'ēn tú, Wéi'ēn tú, Wénshì tú ||
| Venn-Diagramm [n] ||
| Venn diagram || set
| diagramme [m] de Venn ||
| ベン図，ヴェン図 ||
| ベ↓ンず、ヴェ↓ンず ||
|  ||  
|  ||  
| диагра́мма Ве́нна ||
|-
|-
| binary operation, dyadic operation || operation
| 二元运算 ||
| èryuán yùnsuàn ||
| zweistellige Verknüpfung, binäre Verknüpfung ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 572: Line 177:
|  ||  
|  ||  
|  ||  
|  ||  
|-
| binary relation || relation
| 二元关系 ||
| èryuán guānxi ||
| binäre Relation ||
| relation [f] binaire ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
{| 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
|-
|-
| Cantor's theorem || power set; cardinality
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| property of binary operation ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 600: Line 198:
|  ||  
|  ||  
|-
|-
| ||  
| cardinality || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 610: Line 208:
|  ||  
|  ||  
|-
|-
| 反交换律 ||  
| cardinal number || cardinality
| fǎnjiāohuàn lǜ ||
| Antikommutativgesetz [n], Antikommutativität [f] ||
| anticommutative property, anticommutativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|-
| 结合律 ||
| jiéhé lǜ ||
| Assoziativgesetz [n], Assoziativität [f] ||
| associative property, associativity || operation
|  ||  
|  ||  
|  ||  
|  ||  
Line 630: Line 218:
|  ||  
|  ||  
|-
|-
| 交换律 ||
| Cartesian product || ordered pair
| 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 650: Line 228:
|  ||  
|  ||  
|-
|-
| choice function || function; empty set; direct product <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
Line 658: Line 237:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
{| 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
|-
|-
| class || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| operation on set ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 683: Line 248:
|  ||  
|  ||  
|-
|-
| ||  
| codomain, set of destination || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 693: Line 258:
|  ||  
|  ||  
|-
|-
| ||  
| commutative property, commutativity || operation
| ||  
| 交换律 ||  
| ||  
| jiāohuàn lǜ ||  
| absolute complement || complement; subset
| Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f] ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 703: Line 268:
|  ||  
|  ||  
|-
|-
| complement || 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 713: Line 278:
| ра́зность мно́жеств ||  
| ра́зность мно́жеств ||  
|-
|-
| connected relation, total relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| intersection || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 723: Line 288:
|  ||  
|  ||  
|-
|-
| continuum || cardinal number
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| power set, powerset || subset; empty set
|  ||  
|  ||  
|  ||  
|  ||  
Line 733: Line 298:
|  ||  
|  ||  
|-
|-
| converse relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| relative complement || complement; subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 743: Line 308:
|  ||  
|  ||  
|-
|-
| countable set || subset; cardinality
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| union || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 753: Line 318:
|  ||  
|  ||  
|-
|-
| De Morgan's laws || logical conjunction; logical disjunction; negation
|  ||  
|  ||  
|  ||  
|  ||  
Line 761: Line 327:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
{| 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
|-
|-
| ||  
| distributive property, distributivity || operation
| ||  
| 分配律 ||  
| ||  
| fēnpèi lǜ ||  
| system of set theory ||  
| Distributivgesetz [n], Distributivität [f] ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 786: Line 338:
|  ||  
|  ||  
|-
|-
| ||  
| domain, set of departure || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 796: Line 348:
|  ||  
|  ||  
|-
|-
| element || mathematical object
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Zermelo–Fraenkel set theory || axiomatic system
|  ||  
|  ||  
|  ||  
|  ||  
Line 806: Line 358:
|  ||  
|  ||  
|-
|-
| empty set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 814: Line 367:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
{| 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
|-
|-
| enumeration || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| type of set ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 839: Line 378:
|  ||  
|  ||  
|-
|-
| equality ||
| 相等 ||
| xiāng děng ||
| Gleichheit [f] ||
| égalité [f] ||
|  ||  
|  ||  
|  ||  
|  ||  
| تَساوی ||
|  ||  
|  ||  
|-
| equal sign || equality
| 等号 ||
| děng hào ||
| Gleichheitszeichen [n], Ist-gleich-Zeichen [n] ||
| signe [m] égal ||
|  ||  
|  ||  
|  ||  
|  ||  
| عَلَامَتِ مُساوی ||
|  ||  
|  ||  
|-
| equivalence relation || reflexive relation; symmetric relation; transitive relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| countable set || subset; cardinality
|  ||  
|  ||  
|  ||
|-
| expression || digit; symbol
| 表达式, 表示式, 运算式 ||
| biǎodá shì, biǎoshì shì, yùnsuàn shì ||
| Ausdruck [m] ||
| expression [f] ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 859: Line 418:
|  ||  
|  ||  
|-
|-
| extensionality, extensional equality || mathematical object
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| empty set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 869: Line 428:
|  ||  
|  ||  
|-
|-
| finitary relation || Cartesian product
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| finite set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 879: Line 438:
|  ||  
|  ||  
|-
|-
| finite set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| fuzzy set, uncertain set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 889: Line 448:
|  ||  
|  ||  
|-
|-
| ||  
| function || binary relation; set
| ||  
| 函数 ||  
| ||  
| hán shù ||  
| infinite set || set
| Funktion [f] ||  
| ||  
| fonction [f] ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 899: Line 458:
|  ||  
|  ||  
|-
|-
| function space || set; function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| proper subset || subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 909: Line 468:
|  ||  
|  ||  
|-
|-
| fuzzy set, uncertain set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| singleton. unit set || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 919: Line 478:
|  ||  
|  ||  
|-
|-
| identity element, neutral element || binary operation; set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| subset || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 929: Line 488:
|  ||  
|  ||  
|-
|-
| identity function, identity relation, identity map, identity transformation || argument
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| superset || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 939: Line 498:
|  ||  
|  ||  
|-
|-
| image || function; set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| transitive set || subset; urelement
|  ||  
|  ||  
|  ||  
|  ||  
Line 949: Line 508:
|  ||  
|  ||  
|-
|-
| indexed family, family || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| universal set || mathematical object
|  ||  
|  ||  
|  ||  
|  ||  
Line 959: Line 518:
|  ||  
|  ||  
|-
|-
| inequality || equality
| 不等 ||
| bù děng ||
| Ungleichheit [f] ||
| inégalité [f] ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| unordered pair, pair set || set
|  ||  
|  ||  
|-
| infinite set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-founded set || transitive closure
|  ||  
|  ||  
|-
| injection, injective function, one-to-one function || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-ordered set || well-order; total order; non-empty set; least element
|  ||  
|  ||  
|-
| intersection || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
| inverse image, preimage || codomain; subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
{| 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 1,022: Line 568:
|  ||  
|  ||  
|-
|-
| ||  
| logical conjunction ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,032: Line 578:
|  ||  
|  ||  
|-
|-
| logical disjunction ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| connected relation, total relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,042: Line 588:
|  ||  
|  ||  
|-
|-
| mapping || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| converse relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,052: Line 598:
|  ||  
|  ||  
|-
|-
| operand || operation
| 运算数, 运算元 ||
| yùnsuàn shù, yùnsuàn yuán ||
| Operand [m] ||
|  ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| equivalence relation || reflexive relation; symmetric relation; transitive relation
| ||
|-
| operation ||
| 运算 ||
| yùnsuàn ||
| Verknüpfung [f] ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,062: Line 618:
|  ||  
|  ||  
|-
|-
| ordered pair || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| finitary relation || Cartesian product
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,072: Line 628:
|  ||  
|  ||  
|-
|-
| power set, powerset || subset; empty set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| symmetric relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,082: Line 638:
|  ||  
|  ||  
|-
|-
| proper subset || subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| transitive relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,092: Line 648:
|  ||  
|  ||  
|-
|-
| range || codomain; image
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-founded relation || class; minimal element; empty set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,102: Line 658:
|  ||  
|  ||  
|-
|-
| relation || set
| 关系 ||
| guānxi ||
| Relation [f] ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| well-order, well-order relation, well-ordering ||
|  ||  
|  ||  
|  ||  
|  ||  
|-
| relative complement || complement; subset
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,117: Line 677:
|  ||  
|  ||  
|  ||  
|  ||  
|-
| Russell's paradox, Russell's antinomy || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
{| 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 1,145: Line 688:
|  ||  
|  ||  
|-
|-
| ||  
| set || element
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,155: Line 698:
|  ||  
|  ||  
|-
|-
| set difference, difference of set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Boolean function || argument; Boolean domain <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,165: Line 708:
|  ||  
|  ||  
|-
|-
| singleton, unit set ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Boolean-valued function || function; value; Boolean domain <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,175: Line 718:
|  ||  
|  ||  
|-
|-
| subset || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| complex-valued function || function; value; complex number
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,185: Line 728:
|  ||  
|  ||  
|-
|-
| superset || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| functions of several complex variables || argument; complex variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,195: Line 738:
|  ||  
|  ||  
|-
|-
| surjection, surjective function, onto function || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| function of several real variables, real multivariate function || argument; real variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,205: Line 748:
|  ||  
|  ||  
|-
|-
| symmetric difference, disjunctive union || intersection
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integer-valued function || function; value; integer
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,215: Line 758:
|  ||  
|  ||  
|-
|-
| symmetric relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| ordered pair || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,225: Line 768:
|  ||  
|  ||  
|-
|-
| transitive relation || binary relation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| real-valued function || function; value; real number
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,235: Line 778:
|  ||  
|  ||  
|-
|-
| transitive set || subset; urelement
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,243: Line 787:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
=== Axiomatic Set Theory ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| ||  
| tree || partially ordered set; well-ordered set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,268: Line 798:
|  ||  
|  ||  
|-
|-
| tuple || element; sequence
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| amorphous set || infinite set; disjoint union; subset
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,278: Line 808:
|  ||  
|  ||  
|-
|-
| union || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| normal function || ordinal number; monotonically increasing function
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,288: Line 818:
|  ||  
|  ||  
|-
|-
| universal set || mathematical object
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,296: Line 827:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
{| 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
|-
|-
| unordered pair, pair set || set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| axiom of choice || choice function
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,321: Line 838:
|  ||  
|  ||  
|-
|-
| ||  
| urelement || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,331: Line 848:
|  ||  
|  ||  
|-
|-
| Venn diagram || set
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,339: Line 857:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
{| class="wikitable sortable"
|+ theorem in set theory
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| well-founded relation || class; minimal element; empty set
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| theorem in set theory ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,364: Line 868:
|  ||  
|  ||  
|-
|-
| ||  
| well-founded set || transitive closure
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,374: Line 878:
|  ||  
|  ||  
|-
|-
| 康托尔定理 ||  
| Zermelo–Fraenkel set theory || Russel's paradox
| 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 899:
|}
|}


== Proof 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 1,428: Line 922:
|-
|-
|  ||  
|  ||  
|  ||
|  ||
| mathematical induction ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| sequent ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,448: Line 932:
|}
|}


== Model 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 1,473: Line 957:
|  ||  
|  ||  
|  ||  
|  ||  
| elementary equivalence || structure; signature
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,480: Line 964:
|  ||  
|  ||  
|-
|-
| mathematical induction ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| signature || non-logical symbol <logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,493: Line 977:
|  ||  
|  ||  
|  ||  
|  ||  
| structure || cardinality; arity
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,511: Line 995:
|}
|}


== Computability 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 1,544: Line 1,028:
|}
|}


== Type Theory ==
== Computability Theory, Recursion 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 1,569: Line 1,053:
|  ||  
|  ||  
|  ||  
|  ||  
| boolean type || type
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| bottom type || type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,585: Line 1,059:
|  ||  
|  ||  
|  ||  
|  ||  
|}
[[File:Venn-AA_up_Blank.png]]
== * Appendix * ==
=== Adjective & Adjective Phrase; Verb & Verb Phrase ===
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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]
! 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
|-
|-
|  ||  
|  ||  
|  ||
|  ||
| identity type, propositional equality || equality; type
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| product type || type
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| unit type || type
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,626: Line 1,096:
|  ||  
|  ||  
|}
|}
 
=== Symbol ===
== Algebraic Logic ==
==== Set Theory ====
{| class="wikitable sortable"
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! symbol
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! eng-Latn-US: concept
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! cmn-Hans-CN: 概念
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Latn.Pinyin-CN: gàiniàn
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! deu-Latn-DE: Begriff [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! fra-Latn-FR: concept [m]
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Jpan-JP: 概念
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! 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
|
|
|
|
|
|
|
|
|-
|-
| ||  
|  
|  ||  
|  
|  ||  
|  
|  ||  
|  
|  ||  
|  
|  ||  
|  
|  ||  
|  
|  ||  
|  
|  
|  
|}
|}


=== Boolean Algebra ===
=== Process ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! eng-Latn-US: process !! eng-Latn-US: constituent
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: か↑てい !! jpn-Hrkt-JP: こ↑うざい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! pes-Aran-IR: فَرآیَند‎ !! pes-Aran-IR: هَمنِه
! rus-Cyrl-RU: проце́сс !! rus-Cyrl-RU: соста́вная часть
|-
|-
|  ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,668: Line 1,353:
|  ||  
|  ||  
|-
|-
| 德摩根定律 ||
| Dé Mógēn dìnglǜ ||
| De-Morgansche Gesetze [n pl], De-Morgansche Regeln [f pl] ||
| De Morgan's laws || conjunction; disjunction; negation
| lois [f pl] de De Morgan ||
| ド・モルガンの法則 ||
| ド・↑モルガ↓ンのほ↑うそく ||
| зако́ны де Мо́ргана, пра́вила де Мо́ргана ||
|-
|  ||
|  ||
|  ||
| truth table || expression
| table [f] de vérité ||
|  ||
|  ||
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,696: Line 1,364:
|}
|}


<center>
=== Related Free Educational Resources ===
https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn3tab.svg/240px-Venn3tab.svg.png
{| class="wikitable sortable"
</center>
! branch
! name
! link
! language
! public license
|-
|
|
|
|
|
|-
|
|
|
|
|
|}


{{Sci-Tech-Index-Menu}}
{{Sci-Tech-Index-Menu}}
==Other Lessons==
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* [[Language/Multiple-languages/Vocabulary/Electromagnetism|Electromagnetism]]
* [[Language/Multiple-languages/Vocabulary/Must‐Know-Words-for-Polyglots|Must‐Know Words for Polyglots]]
* [[Language/Multiple-languages/Vocabulary/Similarities-between-French-and-Italian|Similarities between French and Italian]]
* [[Language/Multiple-languages/Vocabulary/Statistics|Statistics]]
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]]
* [[Language/Multiple-languages/Vocabulary/I-love-you-in-all-languages|I love you in all languages]]
* [[Language/Multiple-languages/Vocabulary/Emotions-in-many-languages|Emotions in many languages]]
* [[Language/Multiple-languages/Vocabulary/Transparent-Words|Transparent Words]]
* [[Language/Multiple-languages/Vocabulary/Musical-Notes-in-Many-Languages|Musical Notes in Many Languages]]
<span links></span>

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