Language/Multiple-languages/Vocabulary/Mathematical-Logic

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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 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

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
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] 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
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property of binary operation
反交换律 fǎnjiāohuàn lǜ Antikommutativgesetz [n], Antikommutativität [f] anticommutative property, anticommutativity operation
结合律 jiéhé lǜ Assoziativgesetz [n], Assoziativität [f] associative property, associativity operation
交换律 jiāohuàn lǜ Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f] commutative property, commutativity operation
分配律 fēnpèi lǜ Distributivgesetz [n], Distributivität [f] distributive property, distributivity operation
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

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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

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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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