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{| class="wikitable sortable"
{| class="wikitable sortable"
! cmn-Hans-CN: 科目
! cmn-Latn.Pinyin-CN: kēmù
! deu-Latn-DE: Fach [n]
! eng-Latn-US: subject
! fra-Latn-FR: matière [f]
! jpn-Jpan-JP: 科目
! jpn-Hrkt-JP: か↑もく
! rus-Cyrl-RU: предме́т
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| combinatorics
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| graph theory
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| order theory
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| game theory
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== Main ==
=== Combinatorics ===
{| class="wikitable sortable"
! 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]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! 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
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
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|-
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| circular shift || tuple
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|-
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| combination || set <mathematical logic>
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|-
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| factorial || integer <number theory>; non-negative number <number theory>; product <number theory>
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|-
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| permutation || set <mathematical logic>; sequence <number theory>
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|-
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|}
{| class="wikitable sortable"
|+ combinatorial principle
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 144: Line 11:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| discrete mathematics ||
|  ||  
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| combinatorial principle ||
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|-
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|-
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| bijective proof ||
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|-
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| double counting, counting in two ways ||
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|-
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| inclusion–exclusion principle || union <mathematical logic>; intersection <mathematical logic>; cardinality <mathematical logic>
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Line 191: Line 22:
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| method of distinguished element ||
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|-
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| pigeonhole principle ||
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Line 207: Line 29:
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|-
|-
| graph theory ||
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| rule of division ||
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Line 216: Line 38:
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|-
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| order theory ||
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| rule of product, multiplication principle ||
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Line 225: Line 47:
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|-
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| game theory ||
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| rule of sum, addition principle ||
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Line 244: Line 66:
|}
|}


=== Graph Theory ===
== Graph Theory ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 255: Line 77:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
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Line 264: Line 85:
|  ||  
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|-
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| complete graph || undirected graph
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| automorphism || graph; symmetry <geometry>
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|-
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| cycle || trail
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| complete graph || undirected graph
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|-
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| directed cycle || directed trail
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| cycle || trail
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Line 291: Line 109:
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|-
|-
| directed graph, digraph || graph
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| directed cycle || directed trail
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|-
|-
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| directed graph, digraph || graph
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|-
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| edge || vertex
| edge || vertex
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|-
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| edge-labeled graph || edge labeling
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|-
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| endpoint || undirected graph
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| edge labeling || graph labeling
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|-
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| endpoint || undirected graph
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Line 345: Line 134:
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|-
|-
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| graph || set <mathematical logic>; object <mathematical logic>; edge
| graph || set <mathematical logic>; object <mathematical logic>; edge
|  ||  
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|-
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| graph labeling || graph
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|-
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| induced subgraph || subgraph
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| induced subgraph || subgraph
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|-
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| loop || edge
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| loop || edge
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|-
|-
| multigraph || multiple edges
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| multigraph || multiple edges
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|-
|-
| multiple edges, parallel edges || endpoint; tail vertex; head vertex
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| multiple edges, parallel edges || endpoint; tail vertex; head vertex
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|-
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| path || trail
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| path || trail
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|-
|-
| star (graph theory) || complete bipartite graph; tree
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| star (graph theory) || complete bipartite graph; tree
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|-
|-
| subgraph || graph; subset <mathematical logic>
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| subgraph || graph; subset <mathematical logic>
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|-
|-
| supergraph || graph; superset <mathematical logic>
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| supergraph || graph; superset <mathematical logic>
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|-
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| tour || trail
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| tour || trail
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|-
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| trail || walk
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| trail || walk
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|-
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| transpose graph || directed graph
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| transpose graph || directed graph
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|-
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| undirected graph || graph
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| undirected graph || graph
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|-
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| universal vertex, dominating vertex || undirected graph; dominating set
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| universal vertex, dominating vertex || undirected graph; dominating set
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|-
|-
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| vertex [pl:vertices], node ||  
| vertex [pl:vertices], node ||  
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|-
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| vertex labeling || graph labeling
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|-
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| walk || sequence <number theory>; edge
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| vertex-labeled graph || vertex labeling
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|-
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| weight || subgraph
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| walk || sequence <number theory>; edge
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|-
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| weight || subgraph
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Line 537: Line 293:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ perfect graph
|+ perfect graph
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
| perfect graph ||
|  ||
|  ||
|  ||
|  ||
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|-
|-
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| perfect graph ||
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|-
|-
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|-
|-
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Line 576: Line 337:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ theorem in graph theory
|+ theorem in graph theory
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 585: Line 346:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| theorem in graph theory ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
| theorem in graph theory ||
|  ||  
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|-
|-
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Line 603: Line 362:
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|-
|-
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Line 613: Line 371:
|}
|}


=== Order Theory ===
== Order Theory ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 627: Line 385:
|  ||  
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|  ||
|  ||
|  ||
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|-
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|  ||
|  ||
| trichotomy || real number <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 652: Line 400:
|}
|}


=== Game Theory ===
== Game Theory ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 663: Line 411:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
|  ||
|  ||  
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Line 682: Line 429:
|}
|}


== Appendix ==
[[File:640px-Four_Colour_Planar_Graph.svg.png]]
 
== * Appendix * ==
=== Sentence ===
=== Sentence ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! cmn-Hans-CN: 语句 !! cmn-Hans-CN: 前提
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Latn.Pinyin-CN: yǔjù !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! deu-Latn-DE: Satz [m] !! deu-Latn-DE: Voraussetzung [f]
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! eng-Latn-US: sentence !! eng-Latn-US: prerequisite
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! fra-Latn-FR: phrase [f] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 文章 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: ぶ​↑んしょ↓う !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: фра́за !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
|  ||  
|  ||  
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{| class="wikitable sortable"
{| class="wikitable sortable"
! symbol
! symbol
! cmn-Hans-CN: 含义
! eng-Latn-US: concept
! cmn-Latn.Pinyin-CN: hányì
! cmn-Hans-CN: 概念
! deu-Latn-DE: Bedeutung [f]
! cmn-Latn.Pinyin-CN: gàiniàn
! eng-Latn-US: meaning
! deu-Latn-DE: Begriff [m]
! fra-Latn-FR: signification [f]
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 意味
! jpn-Jpan-JP: 概念
! jpn-Hrkt-JP: い​↓​み
! jpn-Hrkt-JP: が↓いねん
! rus-Cyrl-RU: значе́ние
! rus-Cyrl-RU: конце́пция
|-
|-
|  
|  
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=== Process ===
{| class="wikitable sortable"
! 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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|  ||
|}
|}


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<center>
https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Four_Colour_Planar_Graph.svg/400px-Four_Colour_Planar_Graph.svg.png
</center>


{{Sci-Tech-Index-Menu}}
{{Sci-Tech-Index-Menu}}
==Other Lessons==
* [[Language/Multiple-languages/Vocabulary/Theory-of-Inventive-Problem-Solving|Theory of Inventive Problem Solving]]
* [[Language/Multiple-languages/Vocabulary/Language-Autonyms-List|Language Autonyms List]]
* [[Language/Multiple-languages/Vocabulary/No-in-all-languages|No in all languages]]
* [[Language/Multiple-languages/Vocabulary/Similarities-between-French-and-Spanish|Similarities between French and Spanish]]
* [[Language/Multiple-languages/Vocabulary/Collocations-with-take|Collocations with take]]
* [[Language/Multiple-languages/Vocabulary/Structural-Analysis|Structural Analysis]]
* [[Language/Multiple-languages/Vocabulary/Longest-words|Longest words]]
* [[Language/Multiple-languages/Vocabulary/Technical-Drawing|Technical Drawing]]
* [[Language/Multiple-languages/Vocabulary/Computer-Language|Computer Language]]
* [[Language/Multiple-languages/Vocabulary/Days-of-the-week-and-Months-of-the-year|Days of the week and Months of the year]]
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