Language/Multiple-languages/Vocabulary/Mathematical-Logic

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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
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

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
absolute complement	complement; subset
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]
bijection, bijective function, one-to-one correspondence, or invertible function	function, set
axiom of choice	choice function
binary operation, dyadic operation	operation	二元运算		èryuán yùnsuàn		zweistellige Verknüpfung, binäre Verknüpfung
binary relation	relation	二元关系		èryuán guānxi		binäre Relation		relation [f] binaire
cardinality	set
cardinal number	cardinality
choice function	function, empty set, direct product <algebra>
codomain, set of destination	function; set
commutative property, commutativity	operation	交换律		jiāohuàn lǜ		Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f]
complement	set	补集		bǔ jí		Komplement [n]		complémentaire [m]		差集合		さ↑しゅ↓うごう				ра́зность мно́жеств
continuum	cardinal number
countable set	subset; cardinality
distributive property, distributivity	operation	分配律		fēnpèi lǜ		Distributivgesetz [n], Distributivität [f]
domain, set of departure	function; set
element	mathematical object
empty set	set
enumeration	set
equality		相等		xiāng děng		Gleichheit [f]		égalité [f]
equal sign	equality	等号		děng hào		Gleichheitszeichen [n], Ist-gleich-Zeichen [n]		signe [m] égal						علامت مساوی	تساوی
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
finite set	element
function	binary relation; set	函数		hán shù		Funktion [f]		fonction [f]
image	function; set
indexed family, family	set
inequality	equality	不等		bù děng		Ungleichheit [f]		inégalité [f]
intersection	set
inverse image, preimage	codomain; subset
mathematical object
operand	operation	运算数, 运算元		yùnsuàn shù, yùnsuàn yuán		Operand [m]
operation		运算		yùnsuàn		Verknüpfung [f]
map	function
ordered pair	mathematical object
power set, powerset	subset; empty set
proper subset	subset
range	codomain; image
relation	set	关系		guānxi		Relation [f]
relative complement	complement; subset
set	element
subset	set
superset	set
tuple	element; sequence
union	set
unordered pair, pair set	set

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

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

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

* Appendix *

Adjective & Adjective Phrase; Verb & Verb Phrase

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

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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