Difference between revisions of "Language/Multiple-languages/Vocabulary/Mathematical-Logic"
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Revision as of 16:49, 29 January 2022
This is a part of the Sci–Tech Index, a project for science and technology learners.
In progress.
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 | ||||||||||||||||
Cartesian product | ordered pair | ||||||||||||||||
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 | set | ||||||||||||||||
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 | ||||||||||||||||
set difference, difference of set | set | ||||||||||||||||
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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Related Free Educational Resources
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