#noindex
## ==부분순서,partial_order =,partial_order . 부분순서 partial_order
----
Sub:
[[완전부분순서,complete_partial_order,CPO]] =완전부분순서,complete_partial_order,CPO =,complete_partial_order,CPO =,CPO 완전부분순서 complete_partial_order CPO
{
WtEn:complete_partial_order ?
WtEn:CPO ?

// tmp from ([[https://ropas.snu.ac.kr/~jwchoi/talks/snt120601.pdf 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.

i.e.

[[부분순서,partial_order]] 조건 만족
∃,,=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'''. ([[https://ropas.snu.ac.kr/~jwchoi/talks/snt120601.pdf src]])

[[집합,set]] A의 원소들 간에 [[이항관계,binary_relation]] R이 있는데, R이 다음 세 조건을 만족하면, 순서쌍(2-tuple) (A, R)은 '''부분순서집합'''.

ⓐ reflexive relation = reflexive_relation =,reflexive_relation . reflexive_relation
 {
 '''reflexive relation'''
 반사관계 via KmsE:"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 WtEn:reflexive#Adjective instead.

 Up: [[반사성,reflexivity]] =반사성,reflexivity =,reflexivity . 반사성 reflexivity { 반사성 via KmsE:reflexivity WtEn:reflexivity Ggl:reflexivity Up: [[성질,property]](of [[이항관계,binary_relation]] only? QQQ) ... see also https://en.wiktionary.org/wiki/reflexive } [[관계,relation]]
 } // reflexive relation Ggl:"reflexive relation"
ⓑ antisymmetric relation = antisymmetric_relation =,antisymmetric_relation . antisymmetric_relation
 {
 '''antisymmetric relation'''
 반대칭관계 (wk)

 CMP: [[대칭관계,symmetric_relation]]

 WtEn: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 { WtEn:antisymmetry KmsE:antisymmetry Ggl:antisymmetry } // antisymmetry [[관계,relation]]
 } // antisymmetric relation  Ggl:"antisymmetric relation" KmsE:"antisymmetric relation"
ⓒ 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:Transitive_relation = https://en.wikipedia.org/wiki/Transitive_relation
 https://ja.wikipedia.org/wiki/推移関係


 Up: [[transitivity]] ? KmsE:transitive KmsE:transiti

 xxx
 WtEn:transitive_relation = https://en.wiktionary.org/wiki/transitive_relation x [[Date(2023-12-03T20:28:33)]]

 } // transitive relation Ndict:"transitive relation" Ggl:"transitive relation" Bing:"transitive relation"
}

[[partial_order_reduction]]

Up:
[[이항관계,binary_relation]]
[[순서,order]]

[[부분,part]]?

----
<<tableofcontents>>
= Interwikis =
'''''cp from local, [[Date(2023-12-03T19:49:40)]].'''''
https://mathworld.wolfram.com/PartialOrder.html
https://foldoc.org/partial+order
https://planetmath.org/partialorder
https://pub.mearie.org/부분순서
[[https://terms.naver.com/entry.naver?docId=5669177&ref=y&cid=60207&categoryId=60207 수학백과: 부분순서]]
 정의를 보니 [[관계,relation]] esp. [[VG: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

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

----
[[Date(2023-12-17T18:02:09)]]

http://www.gabormelli.com/RKB/Partial_Order_Relation
= autogeninterwikis =
KmsE:"partial order" = https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=partial+order
{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
}

[[WtEn:partial_order]]
= https://en.wiktionary.org/wiki/partial_order

Zeta:부분순서 

Libre:부분순서 
Namu:부분순서 
WpKo:부분순서 

MathWorld:PartialOrder

WpSp:Partial_order
WpEn:Partial_order

WpJa:

...
부분순서 
Ndict:부분순서 Naver:부분순서 Ggl:부분순서 Bing:부분순서 
"partial order" 
Ndict:"partial order" Naver:"partial order" Ggl:"partial order" Bing:"partial order" 

= wikiadmin =
[[Date(2023-12-03T19:49:40)]] Page name via KMS. 저기 반순서도 번역어로 제시되었으나, 반-은 anti-, half- 의미가 강해서 부분순서가 좋겠다.