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

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Revision as of 08:44, 2 March 2022

Hello polyglots, 😀

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

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
set theory 集合论 jíhé lùn Mengenlehre [f] théorie [f] des ensembles 集合論 しゅ↑うご↓うろん тео́рия мно́жеств
axiomatic set theory 公理化集合论 gǒnglǐhuà jíhélùn axiomatische Mengenlehre théorie [f] axiomatique des ensembles 公理的集合論 こ↑うりてき↓しゅ↑うご↓うろん аксиомати́ческая тео́рия мно́жеств
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 тео́рия моде́лей
computability theory, recursion theory 可计算性理论 kějìsuànxìng lǐlùn 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
type theory 类型论 lèixíng lùn Typentheorie [f] théorie [f] des types 型理論 か↑たり↓ろん тео́рией ти́пов
algebraic logic
Boolean algebra algèbre [f] de Boole, algèbre [f] booléenne
relation algebra

Main

Set Theory

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
argument function 参数 cān shù Argument [m] argument [m] 引数 ひ↑きす↓う аксиомати́ческая тео́рия мно́жеств
bijection, bijective function, one-to-one correspondence, or invertible function function; set 双射 shuāng shè Bijektion [f], bijektive Funktion bijection [f] 全単射,双射 ぜ↑んた↓んしゃ,そ↓うしゃ бие́кция
binary operation, dyadic operation operation 二元运算 èryuán yùnsuàn zweistellige Verknüpfung, binäre Verknüpfung opération [f] binaire 二項演算 に↑こうえ↓んざん бина́рная опера́ция, двуме́стная опера́ция
cardinality set 势,浓度 shì, nóng dù Mächtigkeit [f], Kardinalität [f] cardinalité [f] 濃度,カーディナリティ の↓うど,カ↑ーディナ↓リティ мо́щность
cardinal number, cardinal cardinality 基数 jī shù Kardinalzahl [f] nombre cardinal [m], cardinal [m] 基数 き↑す↓う кардина́льное число́
Cartesian product ordered pair 笛卡尔积 Díkǎ'ěr jī kartesisches Produkt, Mengenprodukt [n] produit [m] cartésien 直積,デカルト積 ちょ↑くせ↓き,デ↑カルト­せ↓き прямо́е произведе́ние, дека́ртово произведе́ние
choice function function; empty set; direct product <algebra> 选择函数 xuǎnzé hánshù Auswahlfunktion [f] fonction [f] de choix 選択関数 せ↑んたくか↓んすう фу́нкция вы́бора
class set lèi Klasse [f] classe [f] クラス,類 ク↓ラス,る↓い класс
codomain, set of destination function 到达域,陪域,上域,终域 dàodá yù, péi yù, shàng yù, zhōng yù Zielmenge [f], Wertevorrat [m] ensemble [m] d'arrivée [f] 終域 しゅういき о́бласть значе́ний
continuum cardinal number 连续统 liánxù tǒng Kontinuum [m] continu [m] 連続体 れ↑んぞくたい конти́нуум
domain, set of departure function 定义域 dìngyì yù Definitionsmenge [f], Definitionsbereich [m] ensemble [m] de définition 定義域 て↑いぎ↓いき о́бласть определе́ния
element mathematical object 元素 yuánsù Element [n] élément [m] げ↓ん элеме́нт
enumeration set 列举法 lièjǔ fǎ Aufzählung [f] énumération [f] 数え上げ か↑ぞえあげ перечисле́ние
equality 相等 xiāng děng Gleichheit [f] égalité [f] تَساوی
expression digit; symbol 表达式,表示式,运算式 biǎodá shì, biǎoshì shì, yùnsuàn shì Ausdruck [m] expression [f]
extensionality, extensional equality mathematical object
function binary relation; set 函数 hán shù Funktion [f] fonction [f]
function space set; function
identity element, neutral element binary operation; set
identity function, identity relation, identity map, identity transformation argument
image function; set
indexed family, family set
inequality equality 不等 bù děng Ungleichheit [f] inégalité [f]
injection, injective function, one-to-one function function
inverse image, preimage codomain; subset
mapping function
operand operation 运算数,运算元 yùnsuàn shù, yùnsuàn yuán Operand [m]
operation 运算 yùnsuàn Verknüpfung [f]
ordered pair set
range codomain; image
relation set 关系 guānxi Relation [f]
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>
urelement set
Venn diagram set
axiom of choice
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
axiom of choice choice function
property of binary operation
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
property of binary operation
anticommutative property, anticommutativity operation 反交换律 fǎnjiāohuàn lǜ Antikommutativgesetz [n], Antikommutativität [f]
associative property, associativity operation 结合律 jiéhé lǜ Assoziativgesetz [n], Assoziativität [f]
commutative property, commutativity operation 交换律 jiāohuàn lǜ Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f]
distributive property, distributivity operation 分配律 fēnpèi lǜ Distributivgesetz [n], Distributivität [f]
operation on set
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
operation on set
absolute complement complement; subset
complement. set difference set 补集 bǔ jí Komplement [n] 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
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
system of set theory
Zermelo–Fraenkel set theory axiomatic system
type of set
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
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
binary relation
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
binary relation relation 二元关系 èryuán guānxi binäre 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

Axiomatic Set Theory

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
amorphous set infinite set; disjoint union; subset
theorem in set theory
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
Cantor's theorem power set; cardinality 康托尔定理 Kāngtuō'ěr dìnglǐ Satz [m] von Cantor théorème [m] de Cantor カントールの定理 カ↑ント↓ールの↑て↓いり теоре́ма Ка́нтора

Proof Theory

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
mathematical induction
sequent

Model Theory

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

Computability Theory, Recursion Theory

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

Type Theory

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

Algebraic Logic

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 rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Boolean Algebra

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 rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
De Morgan's laws conjunction; disjunction; negation 德摩根定律 Dé Mógēn dìnglǜ De-Morgansche Gesetze [n pl], De-Morgansche Regeln [f pl] 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

Relation Algebra

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 rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Appendix

Sentence

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

Symbol

Set Theory

symbol eng-Latn-US: concept cmn-Hans-CN: 概念 cmn-Latn.Pinyin-CN: gàiniàn deu-Latn-DE: Begriff [m] 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 eng-Latn-US: concept cmn-Hans-CN: 概念 cmn-Latn.Pinyin-CN: gàiniàn deu-Latn-DE: Begriff [m] 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 eng-Latn-US: concept cmn-Hans-CN: 概念 cmn-Latn.Pinyin-CN: gàiniàn deu-Latn-DE: Begriff [m] 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

eng-Latn-US: process eng-Latn-US: constituent cmn-Hans-CN: 过程 cmn-Hans-CN: 构件 cmn-Latn.Pinyin-CN: guòchéng cmn-Latn.Pinyin-CN: gòujiàn 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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