Difference between r1.45 and the current
@@ -1,3 +1,4 @@
#noindex
[[집합,set]] 이론Up:
@@ -11,11 +12,11 @@
[[자연수의_분할,integer_partition]]// 이 둘은 대비됨
소박한집합론 naive_set_theory https://proofwiki.org/wiki/Definition:Naive_Set_Theory [[WpEn:Naive_set_theory]] '''Naïve set theory'''
공리적집합론 axiomatic_set_theory https://proofwiki.org/wiki/Definition:Axiomatic_Set_Theory
소박한집합론 naive_set_theory https://proofwiki.org/wiki/Definition:Naive_Set_Theory [[WpEn:Naive_set_theory]] { '''naïve set theory / naive set theory''' Rel. WpKo:부랄리포르티_역설 } // "naive set theory" Ggl:"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?
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+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
@@ -27,29 +28,68 @@
see also https://ncatlab.org/nlab/show/material-structural+adjunctiondescriptive_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
Z집합론 Zermelo set theory
// 아래 MKL: axiomatic_set_theory
Z집합론 Zermelo_set_theory ? or Z_set_theory ?
Zermelo set theory
[[WpEn:Zermelo_set_theory]] = https://en.wikipedia.org/wiki/Zermelo_set_theory
https://plato.stanford.edu/entries/zermelo-set-theory/
"Zermelo set theory"Ggl:"Zermelo set theory"
ZF집합론 ZF_set_theory
// [[Ernst_Zermelo]] { Ernst Zermelo WpEn:Ernst_Zermelo }
ZF집합론 ZF_set_theory ? or Zermelo-Fraenkel_set_theory ?
Zermelo-Fraenkel set theory
[[https://terms.naver.com/entry.naver?docId=4125139&cid=60207&categoryId=60207 수학백과 ZF 집합론]]Libre:체르멜로-프렝켈_집합론
"Zermelo-Fraekel set theory"
Ggl:"Zermelo-Fraekel set theory"
[[WpKo:체르멜로-프렝켈_집합론]] = https://ko.wikipedia.org/wiki/체르멜로-프렝켈_집합론
[[WpSp:Zermelo–Fraenkel_set_theory]] = https://simple.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory
[[WpEn:Zermelo–Fraenkel_set_theory]] = https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory
[[WpJa: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"
Ggl:"Zermelo-Fraenkel set theory"
// [[Abraham_Fraenkel]] { Abraham Fraenkel WpEn:Abraham_Fraenkel }
ZF set theory에 [[선택공리,choice_axiom]]만 추가한?
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
von Neumann–Bernays–Gödel set theory (NBG)
ZF의 [[확장,extension]], esp [[conservative_extension]] { conservative extension WpKo:보존적_확장 WpEn:Conservative_extension Up: [[보존,conservation]] [[확장,extension]] }
[[https://terms.naver.com/entry.naver?docId=4125138&cid=60207&categoryId=60207 수학백과 NBG 집합론]] [[WpEn:von_Neumann–Bernays–Gödel_set_theory]]
[[WpJa:フォン・ノイマン＝ベルナイス＝ゲーデル集合論]]
... Ndict:nbg+set+theory Ggl:nbg+set+theoryRelated:
[[논리,logic]]
set_theoretic_programming
'''set theoretic programming'''
집합론적 프로그래밍
[[WpEn:Set_theoretic_programming]]
Ggl:"set theoretic programming"
Up: [[집합론,set_theory]] [[프로그래밍패러다임,programming_paradigm]]
Related/MKL:
[[논리,logic]] esp [[수리논리,mathematical_logic]]
[[사건,event]]
[[수학기초론]]
foundations of mathematics
WpKo:수학기초론
WpEn:Foundations_of_mathematics
WpJa:数学基礎論
[[공리,axiom]]
[[axiom_system]] 공리계 maybe... or 공리체계
[[universe]] =,universe { 전체 .... KmsE:universe }
[[모형,model]] [[모델,model]]
Topics:
[[reflection_principle]] - writing
<<tableofcontents>>
@@ -91,7 +131,8 @@
[[WpKo:드_모르간의_법칙]]
[[WpEn:De_Morgan's_laws]]
Up: [[명제논리,propositional_logic]], [[집합론,set_theory]]
... Ndict:"드 모르간 법칙" Ggl:"드 모르간 법칙"
Up: [[명제논리,propositional_logic]], [[집합론,set_theory]] [[법칙,law]]
}= Bmks ko =
@@ -103,6 +144,10 @@
https://mathvault.ca/hub/higher-math/math-symbols/set-theory-symbols/[[WpEn: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/
----
Twins:
@@ -117,5 +162,4 @@
https://plato.stanford.edu/entries/set-theory/[[Wiki:SetTheory]]
[[https://terms.naver.com/entry.naver?docId=3405344&cid=47324&categoryId=47324 수학백과 집합론]]
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 / 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 }
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 ?
set theoretic programming
집합론적 프로그래밍
Set_theoretic_programming
set theoretic programming
Up: 집합론,set_theory 프로그래밍패러다임,programming_paradigm
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 / naive set theory Rel. 부랄리포르티_역설 } // "naive set theory" naive set theory공리적집합론 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_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 ZermeloErnst_Zermelo }
ZF집합론 ZF_set_theory ? or Zermelo-Fraenkel_set_theory ?Zermelo_set_theory = https://en.wikipedia.org/wiki/Zermelo_set_theoryhttps://plato.stanford.edu/entries/zermelo-set-theory/
"Zermelo set theory"
Zermelo set theory// Ernst_Zermelo { Ernst Zermelo
Ernst_Zermelo }Zermelo-Fraenkel set theory
![[https]](/123/imgs/https.png)
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 FraenkelAbraham_Fraenkel }
ZFC집합론 ZFC_set_theory수학백과 ZF 집합론체르멜로-프렝켈_집합론체르멜로-프렝켈_집합론 = https://ko.wikipedia.org/wiki/체르멜로-프렝켈_집합론Zermelo–Fraenkel_set_theory = https://simple.wikipedia.org/wiki/Zermelo–Fraenkel_set_theoryZermelo–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 extension보존적_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
set_theoretic_programmingZF의 확장,extension, esp conservative_extension { conservative extension
보존적_확장 Conservative_extension Up: 보존,conservation 확장,extension }수학백과 NBG 집합론von_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 theoryset theoretic programming
집합론적 프로그래밍
Set_theoretic_programmingset theoretic programmingUp: 집합론,set_theory 프로그래밍패러다임,programming_paradigm
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
=(A\cup B)\cup C "$A\cup(B\cup C)=(A\cup B)\cup C$")
=(A\cap B)\cap C "$A\cap(B\cap C)=(A\cap B)\cap C$")
분배법칙,distributivity
=(A\cup B)\cap(A\cup C) "$A\cup(B\cap C)=(A\cup B)\cap(A\cup C)$")
=(A\cap B)\cup(A\cap C) "$A\cap(B\cup C)=(A\cap B)\cup(A\cap C)$")
드모르간_법칙,De_Morgan_law
{
De Morgan's laws
^C=A^C\cap B^C "$(A\cup B)^C=A^C\cap B^C$")
^C=A^C\cup B^C "$(A\cap B)^C=A^C\cup B^C$")
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_법칙De_Morgan's_laws...
드 모르간 법칙 드 모르간 법칙Up: 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_relations집합론의 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:
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 theory
https://encyclopediaofmath.org/wiki/Set_theory
https://everything2.com/title/set theory
https://plato.stanford.edu/entries/set-theory/
SetTheory
수학백과 집합론
집합론https://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/
SetTheory수학백과 집합론----
- [1] 수학백과: 부정명제의 3.1.