Language/Multiple-languages/Vocabulary/Mathematical-Logic

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This is a part of the Sci–Tech Index, a project for science and technology learners.

In progress.

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	rus-Cyrl-RU: конце́пция

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-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]	fra-Latn-FR: concept [m]	pes-Aran-IR: مَفهوم

argument	function
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
Cantor's theorem	power set; cardinality
cardinality	set
cardinal number	cardinality
Cartesian product	ordered pair
choice function	function; empty set; direct product <algebra>
class	set
codomain, set of destination	function
continuum	cardinal number
contradiction	proposition
De Morgan's laws	conjunction; disjunction; negation
domain, set of departure	function
element	mathematical object
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
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
tautology	well-formed formula
tree	partially ordered set; well-ordered set
tuple	element; sequence
urelement	set
Venn diagram	set
Zermelo–Fraenkel set theory	Russel's paradox

property of binary operation
eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]
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]

logical connective
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
logical connective, logical operator, sentential connective, sentential operator

conjunction	set
disjunction	set
material biconditional
material conditional, material implication
negation	set

operation on set
eng-Latn-US: concept	eng-Latn-US: prerequisite	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	rus-Cyrl-RU: конце́пция
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

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-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]	fra-Latn-FR: concept [m]
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

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