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

Revision as of 14:31, 20 November 2021

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
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]	jpn-Jpan-JP: 概念	jpn-Hrkt-JP: がいねん	rus-Cyrl-RU: конце́пция
absolute complement	complement; subset
binary operation	element
cardinality	set
codomain, set of destination	function; set
complement	set	补集	bǔ jí	Komplement [n]	complémentaire [m]	差集合	さしゅうごう	ра́зность мно́жеств
continuum	real number <arithmetic>
countable set	subset; cardinality
domain, set of departure	function; set
element	object
empty set	set
enumeration	set
extensionality, extensional equality	object
finite set	element
image	function; set
intersection	set
inverse image, preimage	codomain; subset
map	function
ordered pair	object
power set, powerset	subset; empty set
proper subset	subset
range	codomain; image
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: ぜんたい	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: ぜんたい	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: ぜんたい	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: ぜんたい	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка

Symbol

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	rus-Cyrl-RU: конце́пция
∈	element of
∉	not element of
∋	contain member
∌	not contain member
⊂	subset of; proper subset of
⊃	superset of; proper superset of
⊆	subset of
⊇	superset of
⊄	not subset of; not proper subset of
⊅	not superset of; not proper superset of
⊈	not subset of
⊉	not superset of
⊊	subset and not proper subset of
⊋	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	rus-Cyrl-RU: проце́сс	rus-Cyrl-RU: соста́вная часть

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@@ Line 71: / Line 71: @@
 ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
 |-
-| absolute complement || complement (set theory); subset
+| absolute complement || complement; subset
 |  ||
 |  ||
@@ Line 80: / Line 80: @@
 |  ||
 |-
-| binary operation || element (mathematics)
+| binary operation || element
 |  ||
 |  ||
@@ Line 89: / Line 89: @@
 |  ||
 |-
-| cardinality || set (set theory)
+| cardinality || set
 |  ||
 |  ||
@@ Line 98: / Line 98: @@
 |  ||
 |-
-| codomain, set of destination || function (set theory); set (set theory)
+| codomain, set of destination || function; set
 |  ||
 |  ||
@@ Line 107: / Line 107: @@
 |  ||
 |-
-| complement (set theory) || set (set theory)
+| complement || set
 | 补集 ||
 | bǔ jí ||
-| Komplement [n] (Mengenlehre) ||
+| Komplement [n] ||
-| complémentaire [m] (théorie des ensembles) ||
+| complémentaire [m] ||
 | 差集合 ||
 | さしゅうごう ||
 | ра́зность мно́жеств ||
 |-
-| continuum (set theory) || real number <arithmetic>
+| continuum || real number <arithmetic>
 |  ||
 |  ||
@@ Line 134: / Line 134: @@
 |  ||
 |-
-| domain (set theory), set of departure || function (set theory); set (set theory)
+| domain, set of departure || function; set
 |  ||
 |  ||
@@ Line 143: / Line 143: @@
 |  ||
 |-
-| element (set theory) || object (mathematics)
+| element || object
 |  ||
 |  ||
@@ Line 152: / Line 152: @@
 |  ||
 |-
-| empty set || set (set theory)
+| empty set || set
 |  ||
 |  ||
@@ Line 161: / Line 161: @@
 |  ||
 |-
-| enumeration || set (set theory)
+| enumeration || set
 |  ||
 |  ||
@@ Line 170: / Line 170: @@
 |  ||
 |-
-| extensionality, extensional equality || object (mathematics)
+| extensionality, extensional equality || object
 |  ||
 |  ||
@@ Line 179: / Line 179: @@
 |  ||
 |-
-| finite set || element (set theory)
+| finite set || element
 |  ||
 |  ||
@@ Line 188: / Line 188: @@
 |  ||
 |-
-| image (set theory) || function (set theory); set (set theory)
+| image || function; set
 |  ||
 |  ||
@@ Line 197: / Line 197: @@
 |  ||
 |-
-| intersection (set theory) || set (set theory)
+| intersection || set
 |  ||
 |  ||
@@ Line 206: / Line 206: @@
 |  ||
 |-
-| inverse image (set theory), preimage || codomain; subset
+| inverse image, preimage || codomain; subset
 |  ||
 |  ||
@@ Line 215: / Line 215: @@
 |  ||
 |-
-| map (set theory) || function (set theory)
+| map || function
 |  ||
 |  ||
@@ Line 224: / Line 224: @@
 |  ||
 |-
-| ordered pair || object (mathematics)
+| ordered pair || object
 |  ||
 |  ||
@@ Line 251: / Line 251: @@
 |  ||
 |-
-| range (set theory) || codomain; image (set theory)
+| range || codomain; image
 |  ||
 |  ||
@@ Line 260: / Line 260: @@
 |  ||
 |-
-| relative complement || complement (set theory); subset
+| relative complement || complement; subset
 |  ||
 |  ||
@@ Line 269: / Line 269: @@
 |  ||
 |-
-| set (set theory) || element (set theory)
+| set || element
 |  ||
 |  ||
@@ Line 278: / Line 278: @@
 |  ||
 |-
-| subset || set (set theory)
+| subset || set
 |  ||
 |  ||
@@ Line 287: / Line 287: @@
 |  ||
 |-
-| superset || set (set theory)
+| superset || set
 |  ||
 |  ||
@@ Line 296: / Line 296: @@
 |  ||
 |-
-| tuple || element (mathematics); sequence (mathecatics)
+| tuple || element; sequence
 |  ||
 |  ||
@@ Line 305: / Line 305: @@
 |  ||
 |-
-| union (set theory) || set (set theory)
+| union || set
 |  ||
 |  ||
@@ Line 314: / Line 314: @@
 |  ||
 |-
-| unordered pair, pair set || set (set theory)
+| unordered pair, pair set || set
 |  ||
 |  ||
@@ Line 572: / Line 572: @@
 |-
 | ''A'', ''B'', ''C'', ...
-| set (set theory)
+| set
 |
 |
@@ Line 582: / Line 582: @@
 |-
 | ''a'', ''b'', ''c'', ...
-| element (set theory)
+| element
 |
 |