관계,relation (rev. 1.23)

정의: 집합,set(들)의 cartesian product(곱집합,product_set, VG: 곱집합,product_set )의 부분집합,subset. (mw)

Sub:

// 일단 degree(curr 디그리,degree) / arity(arity) / 대상 집합들의 개수 / .... 기준으로

0인 경우도 존재.
https://en.wikipedia.org/wiki/Relation_of_degree_zero
"relation of degree zero, 0-ary relation, or nullary relation"
// arity / 디그리,degree / 영,zero

1 unary_relation ?

2 이항관계,binary_relation

동치관계,equivalence_relation ->

동치관계,equivalence_relation

3, 4, ...
일반적 명칭? -

n-ary relation 해보니 나오긴 하는데

(misc delme) 철자 혼동 주의: 이하 (in)finitiary 가 아니라 (in)finitary 임

(유한한 수)
finitary_relation =,finitary_relation . finitary_relation

finitary relation

Finitary_relation

finitary relation
~~finitary_relation~~ x 2023-08-22
"finitary relation"

그럼 infinitary_relation 라는 것도 존재?
∞ infinitary_relation

infinitary relation
...
ndict x 2023-08-22

infinitary relation

infinitary relation
https://en.wikipedia.org/wiki/Infinitary_relation - doesn't exist - 2023-08-22
별도 항목으로 따로 둔 사전/백과/위키는 없는 듯 하고 대개 finitary_relation 에서 같이 설명함.
See:
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Cool_Brisk_Walk_Through_Discrete_Mathematics_(Davies)/03:_Relations/3.4:_Finite_and_infinite_relations
직접 관련된건 아니지만 see also:
https://en.wikipedia.org/wiki/Infinitary_combinatorics
rel:
무한집합,infinite_set
"infinitary relation"

-1, -2, ..., 유리수, 실수 이런건 meaningless? cardinal_number에만 의미있음? or expandable?

....

inverse_relation =,inverse_relation . inverse_relation
inverse relation
인버스관계
역관계 ?

inverse_relation x 2023-08-21

Inverse_relation - disambig
https://proofwiki.org/wiki/Definition:Inverse_Relation

inverse relation

inverse relation
인버스,inverse

satisfaction_relation =,satisfaction_relation . satisfaction_relation
{
satisfaction relation

REL
satisfaction =,satisfaction . satisfaction {
만족

이것보다 관련표현인 satisfiability 가 매우 자주 보인다... 아래.

관련표현

satisfactory adj. 만족스러운
satisfiability n. - 보통 '충족가능성'으로 번역하는 게 대세인듯. // or 충족여부 만족가능성 만족여부 ??

satisfiability = https://en.wiktionary.org/wiki/satisfiability
esp Boolean_satisfiability Boolean satisfiability (이걸 줄여서 SAT ?)
satisfiability_problem =,satisfiability_problem . satisfiability_problem

satisfiability problem (이걸 줄여서 SAT ?)
rel conjunctive_normal 논리곱 정규형 ..
Sub
2-SAT
3-SAT
4-SAT etc
the first known NP-complete problem (Stephen_Cook 1971)

https://mathworld.wolfram.com/Satisfaction.html
}

https://planetmath.org/satisfactionrelation

satisfaction relation

satisfaction relation
"satisfaction relation"
} // satisfaction_relation

many-to-one_relation =,many-to-one_relation . many-to-one_relation
{
many-to-one relation
다대일 관계 ?
https://proofwiki.org/wiki/Definition:Many-to-One_Relation

다대일 관계

many-to-one relation
}

many-to-many_relation =,many-to-many_relation . many-to-many_relation
{
다대다 관계?

다대다 관계

many-to-many relation
}

relational_structure =,relational_structure . relational_structure
{
relational structure

relational_structure (x 2023-08-15)
https://xlinux.nist.gov/dads/HTML/relational.html

Relational_structure - redir. to https://en.wikipedia.org/wiki/Structure_(mathematical_logic)

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

aka: relational_system =,relational_system . relational_system { relational system AKA: relational_structure. https://mathworld.wolfram.com/RelationalSystem.html

relational system }
endorelation 으로 정의함. 그게뭐야? not in ndict. 구글해보니 aka homogeneous_relation.

https://ncatlab.org/nlab/show/relational structure

Up: 구조,structure > mathematical_structure

relational structure

relational structure
relational+structure
}

homogeneous_relation =,homogeneous_relation . homogeneous_relation
endorelation =,endorelation . endorelation
{
homogeneous relation
AKA
endorelation

"on a set X is a binary_relation between X and itself" (we)
즉 동일 집합간 이항관계,binary_relation - cartesian product $\displaystyle X\times X$ 의 subset.

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

endorelation

homogeneous relation
}

symmetric_relation =,symmetric_relation =,symmetric_relation . symmetric_relation

symmetric_relation x(2023-08-15)
https://en.wikipedia.org/wiki/Symmetric_relation
symmetric relation
대칭관계 ?

symmetric relation

symmetric relation
"symmetric relation"
Up: 대칭성,symmetry

relation symbol
relation_symbol =,relation_symbol =,relation_symbol . relation_symbol
{
relation symbol
aka: = predicate_symbol = predicate_letter

MKL: 심벌,symbol letter 술어,predicate

via:
https://encyclopediaofmath.org/wiki/Relation_symbol
redir. to
https://encyclopediaofmath.org/wiki/Predicate_symbol

relation symbol

relation symbol
"relation symbol"
}

reflection_relation
reflection relation
https://mathworld.wolfram.com/ReflectionRelation.html

translation_relation
translation relation
https://mathworld.wolfram.com/TranslationRelation.html
짧고 쉬움

recurrence_relation
recurrence relation
https://mathworld.wolfram.com/RecurrenceRelation.html
REL
"When ..., known as recurrence_equation { https://mathworld.wolfram.com/RecurrenceEquation.html } s, or sometimes difference_equation s"
(VG: 점화식,recurrence_relation exists .... 다만 페이지를 점화관계,recurrence_relation recurrence_equation로 나눌 생각을 나도 하는 중.)

universal_relation =,universal_relation . universal_relation
{
universal relation

Universal_relation redir. to: Homogeneous_relation#Particular_homogeneous_relations

보면 empty_relation identity_relation과 cmp tbw

~~universal_relation~~ x 2023-08-23
"universal relation"
}

total_relation - cur at 토털,total

closure_relation =,closure_relation . closure_relation
{

closure_relation x
}

..... ADDHERE ......

[edit]

분야: relation theory ? relational theory ? ¶

relation theory
"relation theory"

Up:
relation_theory =,relation_theory . relation_theory
{
관계론 관계이론

relation_theory

relation

https://proofwiki.org/wiki/Definition:Relation_Theory
https://proofwiki.org/wiki/Category:Relation_Theory

관계,relation 이론,theory
}

... aka relational_theory ?
2023-08-15:

Relational_theory - No, [https]

nlab에서 여기로 링크했으나 아님.

Relation_theory - 페이지없음.

[edit]

MKLINK ¶

[edit]

arity ¶

arity =,arity . arity
{

Arity - "is the number of arguments or operands taken by a function, operation or relation" 즉 함수,function 펑션,function 연산,operation 관계,relation가 가지는 성질. 자료구조,data_structure or ADT : 배열,array등도?

0 nullary
1 unary
2 binary
3 ternary
일반적으로 n-ary

Compare:
차원,dimension
valency ...

Valency_(linguistics)
cardinality ...

Cardinality
}

[edit]