순서,order

Difference between r1.53 and the current

@@ -29,6 +29,12 @@
Sub:
[[조밀순서,dense_order]] - [[조밀성,density]]
[[단항식순서,monomial_order]] - [[단항식,monomial]]
[[순환순서,cyclic_order]] ?
Up: [[순환,cycle]] [[순서,order]]
[[부분순환순서,partial_cyclic_order]] ?
MKL [[부분순서,partial_order]]
[[WpEn:Partial_cyclic_order]]
= https://en.wikipedia.org/wiki/Partial_cyclic_order
ascending_order = increasing_order // WtEn:ascending_order ? WtEn:increasing_order ?
ascending order / increasing order
Twins:
@@ -417,3 +423,6 @@

https://mathworld.wolfram.com/Ordering.html
[[조합,combination]] [[순열,permutation]] (or [[치환,permutation]]) KmsE:permutation
 
[[https://citizendium.org/wiki/Order_(relation)]]



순서,order VG: 순서,order x

기호

순서론,order_theory에선
(일반적인 수학에서 크기를 비교하는) < ...를 쓰기도 하고
휘어진 ≺ .... 를 쓰기도 한다. (이하 8개)
WtEn: U+227A PRECEDES
WtEn: U+227B SUCCEEDS
WtEn: U+227C PRECEDES OR EQUAL TO { precedes or equal to }
WtEn: U+227D SUCCEEDS OR EQUAL TO
and
WtEn: U+227E PRECEDES OR EQUIVALENT TO
WtEn: U+227F SUCCEEDS OR EQUIVALENT TO
WtEn: U+2280 DOES NOT PRECEDE
WtEn: U+2281 DOES NOT SUCCEED
...
TeX로는 https://www.access2science.com/latex/Binary.html 참조.

tmp bmks todel ... via Ggl:
https://math.stackexchange.com/questions/1614875/what-does-≼-or-≺-mean
https://en.wikipedia.org/wiki/Ordered_set_operators

밀접:
인덱스
순서를 가진 것 ~= 인덱스,index를 가진 것

Sub:
조밀순서,dense_order - 조밀성,density
단항식순서,monomial_order - 단항식,monomial
순환순서,cyclic_order ?
ascending_order = increasing_order // WtEn:ascending_order ? WtEn:increasing_order ?
ascending order / increasing order
Twins:
https://oeis.org/wiki/Ascending_order
mkl/cmp: increasing_sequence (curr at 시퀀스,sequence)
Up: ( increment - increment - 증가, 증분,increment , growth )
descending_order // WtEn:descending_order ?
descending order
Twins:
https://oeis.org/wiki/Descending_order
mkl/cmp: decreasing_sequence (curr at 시퀀스,sequence)
Up: ( decrement - decrement - 감소, ..., decay )
순서공리 (rename, 순서공리,order_axiom 순서공리)
order_isomorphism =,order_isomorphism . order_isomorphism
{
order isomorphism
순서동형사상
order isomorphic adj. 순서동형(인) ?? chk
순서동형

순서,order
동형사상,isomorphism

https://en.wikipedia.org/wiki/Order_isomorphism
monotone_function = monotonic_function 의 일종

... Ggl:순서동형

trans comfirmed via KmsK:순서동형 => "order isomorphism 순서동형사상"
WtEn:order_isomorphism x 2024-01-24
} // order isomorphism Ggl:order isomorphism
순서쌍,ordered_pair =순서쌍,ordered_pair =,ordered_pair 순서쌍 ordered_pair //OR//
순서짝,ordered_pair =순서짝,ordered_pair =,ordered_pair 순서짝 ordered_pair //TOO//
{
KmsK:순서쌍
{ as of 2023-10-04
ordered pair 순서쌍, 순서짝
unordered pair 무순서쌍, 순서없는 쌍
}
Ndict:순서쌍


KmsE:ordered pair
https://en.wiktionary.org/wiki/ordered_pair
// VG: 순서쌍,ordered_pair x
"ordered pair"
} // ordered pair 순서쌍/순서짝



순서관계,order_relation - 관계,relation ? 아님 순서가 곧 이항관계? ( Up: 이항관계,binary_relation? )
{w
order relation
순서관계







  • ascending order
  • descending order

/// logic에서의 order
{

일차논리,first-order_logic
RR - curr at 로직,logic?action=highlight&value=1st
VG 일차논리,first-order_logic o


}


(수학 밖)
어순,word_order =어순,word_order =,word_order 어순 word_order ?
{
WtEn:word_order
https://namu.wiki/w/어순
}

z-order =,z-order . z-order
z순서,z-order ?
{
z-order


computer_graphics쪽에서?
} // z-order Ggl:z-order





2. partial order, partially ordered set



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

Sub:

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





Ndict: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
{
WtEn:partially_ordered_set = https://en.wiktionary.org/wiki/partially_ordered_set
WtEn:poset = https://en.wiktionary.org/wiki/poset


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





3. total order, totally ordered set

전순서?
전체순서?

total_order =,total_order =,to .
{
total_order = linear_order
WtEn:total_order
WtEn: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.




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"
Ggl:well ordering principle


4.1.2. 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."

Ggl: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)


7. colexicographic, colexicographical order, colex order

9. pointwise order

pointwise_order
점별순서
점마다순서




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

pointwise}
pointwise+order ... Google:pointwise order Naver:pointwise order

10. order structure

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




12. ADDHERE SUB

13. ADDHERE SUB

14. ADDHERE SUB

15. ADDHERE SUB

16. ADDHERE SUB


17. 같은 영단어 order의 다른 뜻