Editing Language/Multiple-languages/Vocabulary/Mathematical-Logic

{{Sci-Tech-Index-Intro}}

{| class="wikitable sortable"
! 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"
! 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 ==
{| 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
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
| 参数 || 
| cān shù || 
| Argument [m] || 
| argument || function
| argument [m] || 
| 引数 || 
| ひ↑きす↓う || 
|  || 
| аргуме́нт || 
|-
| 双射 || 
| shuāng shè || 
| Bijektion [f], bijektive Funktion || 
| bijection, bijective function, invertible function || function; set
| bijection [f] || 
| 全単射，双射 || 
| ぜ↑んた↓んしゃ，そ↓うしゃ || 
|  || 
| бие́кция || 
|-
| 二元运算 || 
| èryuán yùnsuàn || 
| zweistellige Verknüpfung, binäre Verknüpfung || 
| binary operation, dyadic operation || operation
| opération [f] binaire || 
| 二項演算 || 
| に↑こうえ↓んざん || 
|  || 
| бина́рная опера́ция, двуме́стная опера́ция || 
|-
| 势，浓度 || 
| shì, nóng dù || 
| Mächtigkeit [f], Kardinalität [f] || 
| cardinality || set
| cardinalité [f] || 
| 濃度，カーディナリティ || 
| の↓うど，カ↑ーディナ↓リティ || 
|  || 
| мо́щность || 
|-
| 基数 || 
| jī shù || 
| Kardinalzahl [f] || 
| cardinal number, cardinal || cardinality
| nombre cardinal, cardinal [m] || 
| 基数 || 
| き↑す↓う || 
|  || 
| кардина́льное число́ || 
|-
| 笛卡尔积 || 
| Díkǎ'ěr jī || 
| kartesisches Produkt, Mengenprodukt [n] || 
| Cartesian product || ordered pair
| produit cartésien || 
| 直積，デカルト積 || 
| ちょ↑くせ↓き，デ↑カルトせ↓き || 
|  || 
| прямо́е произведе́ние, дека́ртово произведе́ние || 
|-
| 选择函数 || 
| xuǎnzé hánshù || 
| Auswahlfunktion [f] || 
| choice function || function; empty set; direct product <algebra>
| fonction [f] de choix [m] || 
| 選択関数 || 
| せ↑んたくか↓んすう || 
|  || 
| фу́нкция вы́бора || 
|-
| 类 || 
| lèi || 
| Klasse [f] || 
| class || set
| classe [f] || 
| クラス，類 || 
| ク↓ラス，る↓い || 
|  || 
| класс || 
|-
| 到达域，陪域，上域，终域 || 
| dàodá yù, péi yù, shàng yù, zhōng yù || 
| Zielmenge [f], Wertevorrat [m] || 
| codomain, set of destination || function
| ensemble [m] d'arrivée [f] || 
| 終域 || 
| し↑ゅうい↓き || 
|  || 
| 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] || 
| 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 || 
|  || 
| объёмность [ж] || 
|-
| 单位元 || 
| dānwèi yuán || 
| neutrales Element || 
| identity element, neutral element || binary operation; set
| élément [m] neutre, élément [m] identité || 
| 単位元，中立元 || 
| た↑んいげ↓ん，ちゅ↑うりつげ↓ん || 
|  || 
| нейтра́льный элеме́нт || 
|-
| 恒等函数 || 
| héngděng hánshù || 
| identische Abbildung || 
| identity function, identity relation, identity map, identity transformation || argument
| application [f] identité, fonction [f] identité || 
| 恒等写像 || 
| こ↑うとうしゃ↓ぞう || 
|  || 
| тожде́ственное отображе́ние || 
|-
| 像 || 
| xiàng || 
| Bild [n], Bildbereich [m], Bildmenge [f] || 
| image || function
| image [f] || 
| 像 || 
| ぞ↓う || 
|  || 
| о́браз || 
|-
| 族 || 
| zú || 
| Familie [f] || 
| indexed family, family || set
| famille || 
| 族 || 
| ぞ↑く || 
|  || 
| семе́йство, индекси́рованное семе́йство || 
|-
| 不等 || 
| bù děng || 
| Ungleichheit [f] || 
| inequality || equality
| inégalité [f] || 
| 不等 || 
| ふ↑とう || 
|  || 
| нера́венство || 
|-
| 单射 || 
| dān shè || 
| injektive Funktion || 
| injection, injective function, one-to-one function || function; injectivity
| injection [f] || 
| 単射 || 
| た↑んしゃ || 
|  || 
| инъе́кция, инъекти́вное отображе́ние || 
|-
| 原像 || 
| yuán xiàng || 
| Urbild [n] || 
| inverse image, preimage || codomain; subset
| image [f] réciproque, préimage [f] || 
| 逆像，原像 || 
| ぎゃ↑くぞう，げ↑んぞう || 
|  || 
| обра́тный о́браз, проо́браз || 
|-
| 映射 || 
| yìngshè || 
| Abbildung [f] || 
| mapping || function
| application [f] || 
| 写像 || 
| しゃ↑ぞう || 
|  || 
| отображе́ние || 
|-
| 运算数，运算元 || 
| yùnsuàn shù, yùnsuàn yuán || 
| Operand [m] || 
| operand || operation
| opérande [m] || 
| 被演算子 || 
| ひ↑えんざ↓んし || 
|  || 
| опера́нд  || 
|-
| 运算 || 
| yùnsuàn || 
| Verknüpfung [f] || 
| operation || 
| opération [f] || 
| 演算 || 
| え↑んざん || 
|  || 
| oпера́ция || 
|-
| 序数 || 
| xù shù || 
| Ordinalzahl [f] || 
| ordinal number || enumeration; ordinal numeral <linguistics>
| nombre ordinal || 
| 順序数 || 
| じゅ↑んじょ↓すう || 
|  || 
| поря́дковым число́м, ордина́лом || 
|-
| 值域 || 
| zhí yù || 
| Bild [n] (Funktion), Bildbereich [m] (Funktion), Bildmenge [f] (Funktion) || 
| range || image
| image [f] (application) || 
| 値域 || 
| ち↓いき || 
|  || 
| о́бласть значе́ний, мно́жество значе́ний || 
|-
| 关系 || 
| guānxi || 
| Relation [f] || 
| relation || set
| relation [f] || 
| 関係 || 
| かんけい || 
|  || 
| отноше́ние || 
|-
| 罗素悖论 || 
| Luósù bèilùn || 
| Russellsche Antinomie || 
| Russell's paradox, Russell's antinomy || set
| paradoxe [m] de Russell, antinomie [f] de Russell || 
| ラッセルのパラドックス || 
| ラ↓ッセルのパ↑ラド↓ックス || 
|  || 
| парадо́кс Ра́ссела, антино́мия Ра́ссела || 
|-
| 集合，集 || 
| jíhé, jí || 
| Menge [f] || 
| set || element
| ensemble [m] || 
| 集合 || 
| しゅ↑うごう || 
|  || 
| мно́жество || 
|-
| 满射 || 
| mǎn shè || 
| surjektive Funktion || 
| surjection, surjective function, onto function || function
| surjection [f], application surjective || 
| 全射 || 
| ぜ↑んしゃ || 
|  || 
| сюръе́кция, сюръекти́вное отображе́ние || 
|-
| 对称差 || 
| duìchèn chā || 
| symmetrische Differenz || 
| symmetric difference, disjunctive union || intersection
| différence [f] symétrique || 
| 対称差 || 
| た↑いしょうさ || 
|  || 
| симметри́ческая ра́зность || 
|-
| 多元组 || 
| duōyuán zǔ || 
| Tupel [n] || 
| tuple || element; sequence <number theory>
| uplet [m] || 
| 順序組，組 || 
| じゅ↑んじょぐみ，く↑み || 
|  || 
| корте́ж || 
|-
| 全集 || 
| quán jí || 
| Grundmenge [f], Universum [n] || 
| universe || set
| univers [m] || 
| 宇宙 || 
| う↓ちゅう  || 
|  || 
|  || 
|-
| 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 || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| class="wikitable sortable"
|+ property of binary operation
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
| property of binary operation || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
| 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
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| class="wikitable sortable"
|+ operation on set
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
| operation on set || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| 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
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| class="wikitable sortable"
|+ system of set theory
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
| system of set theory || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| Zermelo–Fraenkel set theory || axiomatic system
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| 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
|-
|  || 
|  || 
|  || 
| 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
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| 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 || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| 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 || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| 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] || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| 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 ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| amorphous set || infinite set; disjoint union; subset
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| normal function || ordinal number; monotonically increasing function
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| class="wikitable sortable"
|+ axiom of choice
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
| axiom of choice || choice function
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| class="wikitable sortable"
|+ theorem in set theory
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
| theorem in set theory || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
| 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 ==
{| 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
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| mathematical induction || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| sequent || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

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

== Computability Theory ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! pes-Aran-IR: مَفهوم !! pes-Aran-IR: پیش‌نیاز
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

== Type 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
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| boolean type || type
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| bottom type || type
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| identity type, propositional equality || equality; type
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| product type || type
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| unit type || type
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

== Algebraic Logic ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

=== Boolean Algebra ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
| 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 || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

<center>
https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn3tab.svg/240px-Venn3tab.svg.png
</center>

{{Sci-Tech-Index-Menu}}

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