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
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				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
amorphous set	infinite set; disjoint union; subset
anticommutative property, anticommutativity	operation	反交换律		fǎnjiāohuàn lǜ		Antikommutativgesetz [n], Antikommutativität [f]
argument	function
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
Cantor's theorem	power set; cardinality
cardinality	set
cardinal number	cardinality
choice function	function; empty set; direct product <algebra>
class	set
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
connected relation, total relation	binary relation
constant function	constant <number theory>; function
continuum	cardinal number
countable set	subset; cardinality
De Morgan's laws	logical conjunction; logical disjunction; negation
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]						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
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
finitary relation	Cartesian product
finite set	set
function	binary relation; set	函数		hán shù		Funktion [f]		fonction [f]
fuzzy set, uncertain set	set
identity function, also called an identity relation, identity map, identity transformation	argument
image	function; set
indexed family, family	set
inequality	equality	不等		bù děng		Ungleichheit [f]		inégalité [f]
infinite set	set
intersection	set
inverse image, preimage	codomain; subset
logical conjunction
logical disjunction
map	function
operand	operation	运算数, 运算元		yùnsuàn shù, yùnsuàn yuán		Operand [m]
operation		运算		yùnsuàn		Verknüpfung [f]
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
Russell's paradox, Russell's antinomy	set
set	element
subset	set
superset	set
symmetric difference, disjunctive union	intersection
symmetric relation	binary relation
transitive relation	binary relation
transitive set	subset; urelement
tree	partially ordered set; well-ordered set
tuple	element; sequence
union	set
universal set	mathematical object
unordered pair, pair set	set
urelement	set
Venn diagram	set
well-founded relation	class; minimal element; empty set
well-founded set	transitive closure
Zermelo–Fraenkel set theory	Russel's paradox

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

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

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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