Up:

수학,math
집합과_확률,set_and_probability
집합,set 이론,theory

Sub:

// 분할,partition:
집합의_분할,set_partition
자연수의_분할,integer_partition

// 이 둘은 대비됨
소박한집합론 naive_set_theory https://proofwiki.org/wiki/Definition:Naive_Set_Theory

Naive_set_theory { naïve set theory / naive set theory Rel.

부랄리포르티_역설 } // "naive set theory"

naive set theory
공리적집합론 axiomatic_set_theory https://proofwiki.org/wiki/Definition:Axiomatic_Set_Theory { mkl 공리,axiom }

// 이 둘도 대비됨.
structural_set_theory https://ncatlab.org/nlab/show/structural set theory ..... 구조적집합론? 구조집합론? { mkl 구조,structure }

zeroth-order_set_theory https://ncatlab.org/nlab/show/zeroth-order set theory
first-order_set_theory https://ncatlab.org/nlab/show/first-order set theory
higher-order_set_theory https://ncatlab.org/nlab/show/higher-order set theory

material_set_theory

AKA membership-based set theory
ex. ZFC
sub - 순집합? 순수집합? ,pure_set https://ncatlab.org/nlab/show/pure set
https://ncatlab.org/nlab/show/material set theory

see also https://ncatlab.org/nlab/show/material-structural adjunction

descriptive_set_theory - 작성중

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

pure_set_theory pure set theory "is a system of set theory in which all elements of sets are themselves sets."(pw) https://proofwiki.org/wiki/Definition:Pure_Set_Theory

// 아래 MKL: axiomatic_set_theory

Z집합론 Zermelo_set_theory ? or Z_set_theory ?

Zermelo set theory

Zermelo_set_theory = https://en.wikipedia.org/wiki/Zermelo_set_theory
https://plato.stanford.edu/entries/zermelo-set-theory/
"Zermelo set theory"

Zermelo set theory
// Ernst_Zermelo { Ernst Zermelo

Ernst_Zermelo }

ZF집합론 ZF_set_theory ? or Zermelo-Fraenkel_set_theory ?

Zermelo-Fraenkel set theory
[https]

수학백과 ZF 집합론(https://terms.naver.com/entry.naver?docId=4125139&cid=60207&categoryId=60207)

체르멜로-프렝켈_집합론

체르멜로-프렝켈_집합론 = https://ko.wikipedia.org/wiki/체르멜로-프렝켈_집합론

Zermelo–Fraenkel_set_theory = https://simple.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory

Zermelo–Fraenkel_set_theory = https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory

ツェルメロ＝フレンケル集合論 = https://ja.wikipedia.org/wiki/ツェルメロ＝フレンケル集合論
https://plato.stanford.edu/entries/set-theory/ZF.html
"Zermelo-Fraenkel set theory"

Zermelo-Fraenkel set theory
// Abraham_Fraenkel { Abraham Fraenkel

Abraham_Fraenkel }

ZFC집합론 ZFC_set_theory

ZF set theory에 선택공리,choice_axiom{ https://encyclopediaofmath.org/wiki/Axiom_of_choice }만 추가한?
https://encyclopediaofmath.org/wiki/ZFC
https://ncatlab.org/nlab/show/ZFC

NBG집합론 NBG_set_theory

von Neumann–Bernays–Gödel set theory (NBG)
ZF의 확장,extension, esp conservative_extension { conservative extension

보존적_확장

Conservative_extension Up: 보존,conservation 확장,extension }
[https]

수학백과 NBG 집합론(https://terms.naver.com/entry.naver?docId=4125138&cid=60207&categoryId=60207)

von_Neumann–Bernays–Gödel_set_theory

フォン・ノイマン＝ベルナイス＝ゲーデル集合論
...

nbg set theory

set_theoretic_programming
set theoretic programming
집합론적 프로그래밍

Set_theoretic_programming

set theoretic programming
Up: 집합론,set_theory 프로그래밍패러다임,programming_paradigm

foundations of mathematics

수학기초론

Foundations_of_mathematics

数学基礎論

공리,axiom
axiom_system 공리계 maybe... or 공리체계
universe =,universe { 전체 ....

universe }
모형,model 모델,model

Topics:
reflection_principle - writing

1. 연산
2. Bmks ko
3. Bmks en

[edit]

1. 연산 ¶

union

$A\cup B=\left{x\middle|x\in A\textrm{ or }x\in B\right}$

intersection

$A\cap B=\left{x\middle|x\in A\textrm{ and }x\in B\right}$
mutually exclusive or disjoint:

$A\cap B=\not\bigcirc$

부분집합,subset
complement

$A^C=\left{x\middle|x\not\in A\right}$

교환법칙,commutativity

$A\cap B=B\cap A$
$A\cup B=B\cup A$

결합법칙,associativity

$A\cup(B\cup C)=(A\cup B)\cup C$
$A\cap(B\cap C)=(A\cap B)\cap C$

분배법칙,distributivity

$A\cup(B\cap C)=(A\cup B)\cap(A\cup C)$
$A\cap(B\cup C)=(A\cap B)\cup(A\cap C)$

드모르간_법칙,De_Morgan_law
{
De Morgan's laws
$(A\cup B)^C=A^C\cap B^C$
$(A\cap B)^C=A^C\cup B^C$

$\neg(p\wedge q)\Leftrightarrow \neg p \vee \neg q$
$\neg(p\vee q)\Leftrightarrow \neg p \wedge \neg q$
이것은 논리곱 ∧과 논리합 ∨사이의 쌍대성,duality.[1]

from (10개의 특강으로 끝내는 수학의 기본 원리)
{

$\sim(A\cup B)=(\sim A)\cap(\sim B)$	합집합의 여집합은 여집합들의 교집합이다.
$\sim(A\cap B)=(\sim A)\cup(\sim B)$	교집합의 여집합은 여집합들의 합집합이다.