1. ordinal (number) ¶

ordinal_number =,ordinal_number . ordinal_number
{
QQQ ordinal number 를 줄여서 ordinal 이라고도?

MKLINK
counting { counting_theorem { https://proofwiki.org/wiki/Counting_Theorem } }
cardinal cardinal_number { https://proofwiki.org/wiki/Definition:Cardinal https://proofwiki.org/wiki/Definition:Cardinal_Number }

ordinal_number
https://proofwiki.org/wiki/Definition:Ordinal
}

2. partial order, partially ordered set ¶

MKLINK
Zorn_lemma
Hasse_diagram

부분순서,partial_order =부분순서,partial_order =,partial_order 부분순서 partial_order
{

Sub:

complete_partial_order

완전부분순서 ? 완전부분순서 완전부분순서
algebraic_complete_partial_order { http://www.pls-lab.org/en/Algebraic_complete_partial_order }

total_order = linear_order
전순서 선형순서 ?
전순서 선형순서 전순서 선형순서
부분순서에, 임의의 두 원소가 비교가능하다는 조건까지 추가된 더 엄격한 순서? chk

러스트,Rust API > trait `std::cmp::PartialOrd
https://doc.rust-lang.org/std/cmp/trait.PartialOrd.html

---

https://planetmath.org/partialorder
https://proofwiki.org/wiki/Definition:Partial_Ordering

부분순서
부분순서
}

부분순서집합,partially_ordered_set OR
부분순서집합,partially_ordered_set,poset
=부분순서집합,partially_ordered_set,poset =,partially_ordered_set =,poset . 부분순서집합 partially_ordered_set poset
{
partially_ordered_set = https://en.wiktionary.org/wiki/partially_ordered_set
poset = https://en.wiktionary.org/wiki/poset

Sub: complately_partially_ordered_set ? { https://en.wikipedia.org/wiki/Complete_partial_order }

---

https://en.wikipedia.org/wiki/Partially_ordered_set

https://artofproblemsolving.com/wiki/index.php/Partially_ordered_set
https://encyclopediaofmath.org/wiki/Partially_ordered_set
https://proofwiki.org/wiki/Definition:Partially_Ordered_Set
}

3. total order, totally ordered set ¶

전순서?
전체순서?

total_order =,total_order =,to .
{
total_order = linear_order
total_order
linear_order

"is a partial_order in which any two elements are comparable"(we)

Sub:

strict_total_order
strict_linear_order
non-strict_total_order
non-strict_linear_order
see https://en.wikipedia.org/wiki/Total_order#Strict_and_non-strict_total_orders

러스트,Rust API > trait std::cmp::ord
https://doc.rust-lang.org/std/cmp/trait.Ord.html
Trait for types that form a total order.

Twin
https://en.wikipedia.org/wiki/Total_order
... total.order
Up: partial_order
}

totally_ordered_set
{
https://encyclopediaofmath.org/wiki/Totally_ordered_set - chain, linear order // 사슬,chain 선형순서,linear_order
https://proofwiki.org/wiki/Definition:Totally_Ordered_Set
}

https://proofwiki.org/wiki/Definition:Total_Ordering

4. well ¶

4.1. well-ordering ¶

4.1.1. well-ordering principle ¶

well-ordering principle or well ordering principle
well-ordering_principle or well_ordering_principle

Twin

https://artofproblemsolving.com/wiki/index.php/Well_Ordering_Principle

"every nonempty subset of the positive integers $\displaystyle \mathbb{Z}^{+}$ contains a smallest element."
rel mathematical_induction ie 귀납,induction(of math)

...
"well ordering principle"
well ordering principle

isa 원리,principle

4.1.2. well-ordering theorem ¶

well-ordering_theorem =,well-ordering_theorem =,well-ordering_theorem . well-ordering_theorem
well-ordering theorem

well-ordering_theorem

https://en.wikipedia.org/wiki/Well-ordering_theorem

"the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered."

well-ordering theorem
"well-ordering theorem"

4.2. well-ordered set, woset ¶

well-ordered_set =,well-ordered_set =,well-ordered_set . well-ordered_set
well-ordered set
https://encyclopediaofmath.org/wiki/Well-ordered_set
{
이항관계,binary_relation ≤와 집합과 네 조건으로 정의함.
}
https://proofwiki.org/wiki/Definition:Well-Ordered_Set
(Redirected from Definition:Woset i.e. https://proofwiki.org/wiki/Definition:Woset)

well-ordered set
well-ordered set
well-ordered set
"well-ordered set"

5. lexicographic order ¶

6. reverse lexicographic order ¶

7. colexicographic, colexicographical order, colex order ¶

8. preorder #preorder ¶

9. pointwise order ¶

pointwise_order
점별순서
점마다순서

at 2023-08-08
pointwise_order - none.
Pointwise_order - redir to Pointwise#Pointwise_relations
pointwise order
pointwise
pointwise*

Up: pointwise
{
pointwise
Prefix for mathematical terms?
// kms pointwise : '점마다, 점별' .... https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=pointwise pointwise
Cmp: piecewise
{
piecewise
// kms piecewise : 조각/조각마다/조각적 ... https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=piecewise piecewise
// kms wise : https://www.kms.or.kr/mathdict/list.html?key=ename&keyword=wise
.....
piecewise
wise
}

Sub:
pointwise_order =,pointwise_order . pointwise_order
{ pointwise order
pointwise+order
}
pointwise_relation =,pointwise_relation . pointwise_relation
{ pointwise relation
Pointwise#Pointwise_relations
pointwise+relation
}
pointwise_operation =,pointwise_operation . pointwise_operation
{
... pointwise operation pointwise operation
}

pointwise}
pointwise+order ... pointwise order pointwise order

10. order structure ¶

order structure
order_structure =,order_structure =,order_structure . order_structure
=순서구조,order_structure ? is a 구조,structure?

order_structure ?
order_structure ?
order_structure ?

https://en.wikipedia.org/wiki/List_of_order_structures_in_mathematics

순서구조
order structure

11. alphabetical order ¶

alphabetical_order
alphabetical_order
alphabetical order

Rel 알파벳,alphabet

12. ADDHERE SUB ¶

13. ADDHERE SUB ¶

14. ADDHERE SUB ¶

15. ADDHERE SUB ¶

16. ADDHERE SUB ¶

17. 같은 영단어 order의 다른 뜻 ¶

오더,order
...
order

18. 비슷? / 비교 ¶

Similar:
순위,rank or 랭크,rank

---

http://emal.iptime.org/noriwiki/index.php/Order

https://oeis.org/wiki/Orderings

https://mathworld.wolfram.com/Ordering.html

조합,combination 순열,permutation (or 치환,permutation) permutation

https://citizendium.org/wiki/Order_(relation)