열거,enumeration

열거,enumeration (rev. 1.12)

Contents

1. enumeration operator

2. enumeration reducibility

3. enumeration algorithm

4. recursively enumerable (adj.) (prefix)

4.1. recursively enumerable set
4.2. recursively enumerable
4.3. recursively enumerable
4.4. recursively enumerable language

5.1. C#
5.2. Python

7. Misc, etc

7.1. enumerative geometry
7.2. enumerative combinatorics

cmp countable
n. enumerability ?

개념상 당연히 다음과 매우 밀접
{
이산성 discreteness
자연수 natural_number ℕ
정수 integer ℤ
counting 세기/카운팅/셈/...
successor 다음수함수 ?
numbering ... =,numbering numbering

{

numbering
넘버링
번호매기기?
...말고?

Numbering_(computability_theory) = https://en.wikipedia.org/wiki/Numbering_(computability_theory)

첫문장(2023-12-18)
"In computability theory
// 계산가능성이론,computability_theory에서
a numbering is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some formal language."
// '''numbering''이란, 자연수,natural_numbers들을 객체/대상(objects)들의 집합에 할당,assignment하는 것.

} //numbering

} // enumeration과 밀접한것들

그래서 적용 가능한 대상은
{
ℕ ℤ 그 자체는 물론이고
integer 인덱스,index로 접근가능한 모든것들
...
}

rel, mklink:
계산가능성,computability
계산가능성이론,computability_theory

1. enumeration operator ¶

enumeration_operator =,enumeration_operator . enumeration_operator
enumeration operator

열거,enumeration operator ...
열거 operator(오퍼레이터,operator 연산자,operator 작용소,operator)

https://encyclopediaofmath.org/wiki/Enumeration_operator

mentions
recursively-enumerable_set = recursively-enumerable set ...

recursively-enumerable set

recursively-enumerable set
보통 그냥 띄어쓰는듯
recursively_enumerable_set = recursively enumerable set ...

recursively enumerable set
아무튼
=,recursively-enumerable_set =,recursively_enumerable_set
https://mathworld.wolfram.com/RecursivelyEnumerableSet.html
https://ko.wikipedia.org/wiki/재귀_열거_집합
https://en.wikipedia.org/wiki/Computably_enumerable_set
재귀 열거가능 집합 ?
재귀 열거 집합 ? (wk)

재귀 열거가능 집합

재귀 열거 집합

재귀 열거가능 집합

재귀 열거 집합
집합,set

....

enumeration operator

via partial recursive operator partial_recursive_operator https://encyclopediaofmath.org/wiki/Partial_recursive_operator
via partial recursive function / recursive function / computable function 셋중에하나

2. enumeration reducibility ¶

enumeration_reducibility =,enumeration_reducibility . enumeration_reducibility
{
enumeration reducibility
https://en.wikipedia.org/wiki/Enumeration_reducibility

enumeration reducibility
}

3. enumeration algorithm ¶

enumeration_algorithm - at local

Enumeration_algorithm = https://en.wikipedia.org/wiki/Enumeration_algorithm
알고리듬,algorithm

4. recursively enumerable (adj.) (prefix) ¶

적절한 명사형?

recursively_enumerable

recursively enumerable

recursively enumerable

4.1. recursively enumerable set ¶

recursively_enumerable_set
// 이건 이 파일 위로 //

4.2. recursively enumerable ¶

recursively_enumerable_

4.3. recursively enumerable ¶

recursively_enumerable_

4.4. recursively enumerable language ¶

recursively_enumerable_language =,recursively_enumerable_language . recursively_enumerable_language

재귀 열거 언어 / 재귀적 열거 가능 언어 (wk)

촘스키_위계,Chomsky_hierarchy에서 type-0 언어,language.

https://ko.wikipedia.org/wiki/재귀_열거_언어

recursively enumerable language

5. PL ¶

이때는 보통 그 '열거형'과 관련 신택스,syntax.

표현이 많은데 별 언급할필요는 없으나 주의점같은거 있음 write..
enumerations
enumerated|enumeration (data) type

5.1. C# ¶

enumeration_type

https://learn.microsoft.com/en-us/dotnet/csharp/language-reference/builtin-types/enum

System.Enum type => https://learn.microsoft.com/en-us/dotnet/api/system.enum
은 모든 enumeration types의 abstract_base_class

5.2. Python ¶

파이썬,Python
{
enum
https://docs.python.org/ko/3.9/library/enum.html
이건 클래스? 타입? 임.

먼저
from enum import Enum
로 import한다음, 그걸 상속받는 클래스를 만든다.

class Sth(Enum):
 ...

..

enumerate
이건 함수임.
원소마다 순서,order 값을 부여해줌.
..

python enumerate

}

6. MKLINK ¶

가부번집합,denumerable_set

7. Misc, etc ¶

7.1. enumerative geometry ¶

(geometry)
enumerative_geometry =,enumerative_geometry .
{
enumerative geometry
열거기하
열거기하학
(we) "enumerative geometry is the branch of algebraic_geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection_theory."

열거_기하학 = https://ko.wikipedia.org/wiki/열거_기하학

Enumerative_geometry
https://ncatlab.org/nlab/show/enumerative geometry
Up: algebraic_geometry
enumerative+geometry
}

7.2. enumerative combinatorics ¶

enumerative combinatorics
열거조합론 ?

enumerative_combinatorics

enumerative_combinatorics ?

Enumerative_combinatorics = https://en.wikipedia.org/wiki/Enumerative_combinatorics

...
"enumerative combinatorics"

enumerative combinatorics

enumerative combinatorics
enumerative+combinatorics

Up: 열거,enumeration 조합론,combinatorics

8. Interw ¶

https://encyclopediaofmath.org/wiki/Enumeration