Sub:
부분순환순서,partial_cyclic_order ? - Rel 순환순서,cyclic_order
완전부분순서,complete_partial_order,CPO =완전부분순서,complete_partial_order,CPO =,complete_partial_order,CPO =,CPO 완전부분순서 complete_partial_order CPO
{

CPO ?

// tmp from ( [https]

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]

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

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 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_relation

{
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 관계,relation
} // antisymmetric relation

antisymmetric relation

{
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

}

partial_order_reduction

Up:
이항관계,binary_relation
순서,order

부분,part?

1. Interwikis
2. autogeninterwikis
3. wikiadmin

[edit]

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
[https]

수학백과: 부분순서

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

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

2023-12-18

http://www.gabormelli.com/RKB/Partial_Order_Relation

[edit]

2. autogeninterwikis ¶

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
}

partial_order
= https://en.wiktionary.org/wiki/partial_order