Sub:
완전부분순서,complete_partial_order,CPO =완전부분순서,complete_partial_order,CPO =,complete_partial_order,CPO =,CPO 완전부분순서 complete_partial_order CPO
{
complete_partial_order ?
CPO ?
완전부분순서,complete_partial_order,CPO =완전부분순서,complete_partial_order,CPO =,complete_partial_order,CPO =,CPO 완전부분순서 complete_partial_order CPO
{
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
// tmp from (
src)
{
CPO, Complete Partial Order
Partial ordering에, Additional conditions가 붙은 것:
1 There exists a least element, usually written as ⊥.
2 Every chain has a least upper bound.
![[https]](/wiki/imgs/https.png)
{
CPO, Complete Partial Order
Partial ordering에, Additional conditions가 붙은 것:
1 There exists a least element, usually written as ⊥.
2 Every chain has a least upper bound.
i.e.
부분순서,partial_order 조건 만족
∃=1 least_element // least_element
∀사슬,chain has_a : 최소상계,least_upper_bound
∃=1 least_element // least_element
∀사슬,chain has_a : 최소상계,least_upper_bound
}
} // CPO
부분순서집합,partially_ordered_set,poset
{
Binary relation R in a set A which is reflexive, antisymmetric, and transitive. / The pair (A, R) is called a poset. (
src)
{
Binary relation R in a set A which is reflexive, antisymmetric, and transitive. / The pair (A, R) is called a poset. (
![[https]](/wiki/imgs/https.png)
ⓐ reflexive relation = reflexive_relation =,reflexive_relation . reflexive_relation
{
reflexive relation
반사관계 via
reflexive relation
임의의 원소 a에 대해 aRa를 만족하는 이항관계. (wk)
Twin
https://ko.wikipedia.org/wiki/반사관계
https://simple.wikipedia.org/wiki/Reflexive_relation
https://en.wikipedia.org/wiki/Reflexive_relation
https://ja.wikipedia.org/wiki/反射関係
xxx
https://en.wiktionary.org/wiki/reflexive_relation x 2023-12 ... see
reflexive#Adjective instead.
Up: 반사성,reflexivity =반사성,reflexivity =,reflexivity . 반사성 reflexivity { 반사성 via
reflexivity
reflexivity
reflexivity Up: 성질,property(of 이항관계,binary_relation only? QQQ) ... see also https://en.wiktionary.org/wiki/reflexive } 관계,relation
} // reflexive relation
reflexive relation
ⓑ antisymmetric relation = antisymmetric_relation =,antisymmetric_relation . antisymmetric_relationreflexive relation
반사관계 via
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
임의의 원소 a에 대해 aRa를 만족하는 이항관계. (wk)
Twin
https://ko.wikipedia.org/wiki/반사관계
https://simple.wikipedia.org/wiki/Reflexive_relation
https://en.wikipedia.org/wiki/Reflexive_relation
https://ja.wikipedia.org/wiki/反射関係
xxx
https://en.wiktionary.org/wiki/reflexive_relation x 2023-12 ... see
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
Up: 반사성,reflexivity =반사성,reflexivity =,reflexivity . 반사성 reflexivity { 반사성 via
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
} // reflexive relation
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
{
antisymmetric relation
반대칭관계 (wk)
CMP: 대칭관계,symmetric_relation
antisymmetric_relation ?
https://mathworld.wolfram.com/AntisymmetricRelation.html
https://ncatlab.org/nlab/show/antisymmetric relation
https://ko.wikipedia.org/wiki/반대칭관계
https://en.wikipedia.org/wiki/Antisymmetric_relation
Up: antisymmetry ?? =,antisymmetry . antisymmetry {
antisymmetry
antisymmetry
antisymmetry } // antisymmetry 관계,relation
} // antisymmetric relation
antisymmetric relation
antisymmetric relation
ⓒ transitive relation = transitive_relation =,transitive_relation . transitive_relationantisymmetric relation
반대칭관계 (wk)
CMP: 대칭관계,symmetric_relation
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://mathworld.wolfram.com/AntisymmetricRelation.html
https://ncatlab.org/nlab/show/antisymmetric relation
https://ko.wikipedia.org/wiki/반대칭관계
https://en.wikipedia.org/wiki/Antisymmetric_relation
Up: antisymmetry ?? =,antisymmetry . antisymmetry {
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
} // antisymmetric relation
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
{
transitive relation
추이적 관계 (wk)
추이적관계
추이관계
심플. aRb ∧ bRc → aRc 이면 추이적인 관계.
https://ko.wikipedia.org/wiki/추이적_관계
Transitive_relation = https://en.wikipedia.org/wiki/Transitive_relation
https://ja.wikipedia.org/wiki/推移関係
Up: transitivity ?
transitive
transiti
xxx
transitive_relation = https://en.wiktionary.org/wiki/transitive_relation x 2023-12-04
} // transitive relation
transitive relation
transitive relation
transitive relation
}transitive relation
추이적 관계 (wk)
추이적관계
추이관계
심플. aRb ∧ bRc → aRc 이면 추이적인 관계.
https://ko.wikipedia.org/wiki/추이적_관계
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
https://ja.wikipedia.org/wiki/推移関係
Up: transitivity ?
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
xxx
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
} // transitive relation
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
1. Interwikis ¶
cp from local, 2023-12-04.
https://mathworld.wolfram.com/PartialOrder.html
https://foldoc.org/partial order
https://planetmath.org/partialorder
https://pub.mearie.org/부분순서
수학백과: 부분순서
https://mathworld.wolfram.com/PartialOrder.html
https://foldoc.org/partial order
https://planetmath.org/partialorder
https://pub.mearie.org/부분순서
![[https]](/wiki/imgs/https.png)
정의를 보니 관계,relation esp.
관계,relation#s-11(순서관계,order_relation ?)를 연상시키는, 즉 매우 매우 비슷한데, 정확히 어떻게 되는지 study and tbw.
https://ncatlab.org/nlab/show/partial order![VG: VG:](/wiki/imgs/interwiki/vg-16.png)
https://everything2.com/title/partial order
http://wiki.c2.com/?PartialOrder
https://en.wikipedia.org/wiki/Partially_ordered_set#Partial_order
https://xlinux.nist.gov/dads/HTML/partialorder.html
http://wiki.c2.com/?PartialOrder
https://en.wikipedia.org/wiki/Partially_ordered_set#Partial_order
https://xlinux.nist.gov/dads/HTML/partialorder.html
2023-12-18
2. autogeninterwikis ¶
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
{2023-12-04
partial order 반순서, 부분순서
partial ordered set 반순서집합, 부분순서집합
partial ordering 반순서, 부분순서
partial ordering relation 반순서관계, 부분순서관계
strict partial order 순부분순서
}
WpJa:
...
부분순서
부분순서
부분순서
부분순서
부분순서
"partial order"
partial order
partial order
partial order
partial order
부분순서
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"partial order"
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)