집합,set 이론
Up:
Sub:
논리,logic esp 수리논리,mathematical_logic
사건,event
수학기초론
공리,axiom
axiom_system 공리계 maybe... or 공리체계
universe =,universe { 전체 .... universe }
모형,model 모델,model
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
공리적집합론 axiomatic_set_theory https://proofwiki.org/wiki/Definition:Axiomatic_Set_Theory
// 이 둘도 대비됨.
structural_set_theory https://ncatlab.org/nlab/show/structural set theory ..... 구조적집합론? 구조집합론?
descriptive_set_theory - 작성중
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 ?
Related/MKL: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
공리적집합론 axiomatic_set_theory https://proofwiki.org/wiki/Definition:Axiomatic_Set_Theory
// 이 둘도 대비됨.
structural_set_theory https://ncatlab.org/nlab/show/structural set theory ..... 구조적집합론? 구조집합론?
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_theoryfirst-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
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 adjunctionex. ZFC
sub - 순집합? 순수집합? ,pure_set https://ncatlab.org/nlab/show/pure set
https://ncatlab.org/nlab/show/material set theory
descriptive_set_theory - 작성중
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_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 }
Zermelo-Fraenkel set theory
수학백과 ZF 집합론
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_theory수학백과 ZF 집합론
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 }
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_theoryhttps://encyclopediaofmath.org/wiki/ZFC
https://ncatlab.org/nlab/show/ZFC
von Neumann–Bernays–Gödel set theory (NBG)
ZF의 확장,extension, esp conservative_extension { conservative extension 보존적_확장 Conservative_extension Up: 보존,conservation 확장,extension }
수학백과 NBG 집합론
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 nbg set theory
ZF의 확장,extension, esp conservative_extension { conservative extension 보존적_확장 Conservative_extension Up: 보존,conservation 확장,extension }
수학백과 NBG 집합론
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 nbg set theory
논리,logic esp 수리논리,mathematical_logic
사건,event
수학기초론
공리,axiom
axiom_system 공리계 maybe... or 공리체계
universe =,universe { 전체 .... universe }
모형,model 모델,model
1. 연산 ¶
union
intersection
mutually exclusive or disjoint:
부분집합,subset
complement
교환법칙,commutativity
결합법칙,associativity
분배법칙,distributivity
드모르간_법칙,De_Morgan_law
{
De Morgan's laws
mutually exclusive or disjoint:
complement
{
De Morgan's laws
from (10개의 특강으로 끝내는 수학의 기본 원리)
{
}
{
합집합의 여집합은 여집합들의 교집합이다. | |
교집합의 여집합은 여집합들의 합집합이다. |
드_모르간의_법칙
De_Morgan's_laws
... 드 모르간 법칙 드 모르간 법칙
Up: 명제논리,propositional_logic, 집합론,set_theory 법칙,law
}
De_Morgan's_laws
... 드 모르간 법칙 드 모르간 법칙
Up: 명제논리,propositional_logic, 집합론,set_theory 법칙,law
}
3. Bmks en ¶
List_of_set_identities_and_relations = https://en.wikipedia.org/wiki/List_of_set_identities_and_relations
집합론의 역사 관련 (tmp)
The Early Development of Set Theory (Stanford Encyclopedia of Philosophy)
https://plato.stanford.edu/entries/settheory-early/
The Early Development of Set Theory (Stanford Encyclopedia of Philosophy)
https://plato.stanford.edu/entries/settheory-early/
Twins:
https://encyclopediaofmath.org/wiki/Set_theory
https://everything2.com/title/set theory
https://plato.stanford.edu/entries/set-theory/
SetTheory
수학백과 집합론
집합론
https://en.citizendium.org/wiki/Set_theory
https://planetmath.org/settheory
https://mathworld.wolfram.com/SetTheory.html
https://proofwiki.org/wiki/Definition:Set_Theory
https://ncatlab.org/nlab/show/set theoryhttps://en.citizendium.org/wiki/Set_theory
https://planetmath.org/settheory
https://mathworld.wolfram.com/SetTheory.html
https://proofwiki.org/wiki/Definition:Set_Theory
https://encyclopediaofmath.org/wiki/Set_theory
https://everything2.com/title/set theory
https://plato.stanford.edu/entries/set-theory/
SetTheory
수학백과 집합론
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- [1] 수학백과: 부정명제의 3.1.