Difference between r1.43 and the current
@@ -46,10 +46,17 @@
https://encyclopediaofmath.org/wiki/Axiom_of_choice
[[Namu:선택공리]]
WpKo:선택_공리
분리공리? separation_axiom
https://artofproblemsolving.com/wiki/index.php/Separation_axioms
[[귀납공리,induction_axiom]] - [[귀납,induction]] - curr at [[VG:귀납,induction]]
{
[[Namu:선택공리]]
WpKo:선택_공리
}// 선택공리 .... NN:선택공리
[[분리공리,separation_axiom]]
{
'''axiom of separation'''
[[위상,topology]] [[separation]] [[공리,axiom]]
https://ncatlab.org/nlab/show/axiom+of+separation
[[위상,topology]] [[분리,separation]] [[공리,axiom]]
}// axiom of separation .... NN:"axiom of separation" Naver:"axiom of separation" Bing:"axiom of separation" Ggl:"axiom of separation"
[[귀납공리,induction_axiom]] - [[귀납,induction]] - curr at [[VG:귀납,induction]]
{
@@ -152,18 +159,7 @@
[[WpKo:페아노_공리계]] = https://ko.wikipedia.org/wiki/페아노_공리계
... Google:Peano+axioms
rel
[[WpEn:Natural_number#Peano_axioms]]
[[WpEn:Peano_axioms]]
= https://en.wikipedia.org/wiki/Peano_axioms
[[WpJa:ペアノの公理]]
https://ja.wikipedia.org/wiki/ペアノの公理
...
"페아노 공리"
Ndict:"페아노 공리"
Naver:"페아노 공리"
Ggl:"페아노 공리"
rel
Z공리계 ?
... Google:Peano+axioms
rel
[[페아노_공리,Peano_axiom]] =페아노_공리,Peano_axiom =,Peano_axiom 페아노_공리 Peano_axiom
[[페아노_공리,Peano_axiom]]
[[페아노_산술,Peano_arithmetic]]Z공리계 ?
@@ -268,7 +264,9 @@
= Twins =
https://artofproblemsolving.com/wiki/index.php/Axiom
https://mathworld.wolfram.com/Axiom.html
https://en.wikipedia.org/wiki/Category:Mathematical_axioms
https://www.proofwiki.org/wiki/Category:Axioms
https://artofproblemsolving.com/wiki/index.php/Axiom
https://mathworld.wolfram.com/Axiom.html
https://ncatlab.org/nlab/show/axiom
https://en.wikipedia.org/wiki/Category:Mathematical_axioms
https://www.proofwiki.org/wiki/Category:Axioms
5를 부정해도 consistent ? 이걸 부정하면 : 비유클리드_기하학,non-Euclidean_geometry
Sub ¶
확장공리,extension_axiom? 확장,extension?
선택공리,choice_axiom axiom of choice, AoC
{
귀납,induction 공리,axiom
{
axiom of extension
AKA
axiom of extensionality, and
axiom of extent[1]
Via https://proofwiki.org/wiki/Definition:Set_Equality#Axiom_of_Extension
https://proofwiki.org/wiki/Axiom:Axiom_of_Extension
https://proofwiki.org/wiki/Axiom:Axiom_of_Extension/Set_Theory
}// axiom of extension ... axiom of extension axiom of extension
순서공리,order_axiom - 이미있는페이지 순서공리 - axiom of order ? - rel. 순서,orderaxiom of extension
AKA
axiom of extensionality, and
axiom of extent[1]
Via https://proofwiki.org/wiki/Definition:Set_Equality#Axiom_of_Extension
https://proofwiki.org/wiki/Axiom:Axiom_of_Extension
https://proofwiki.org/wiki/Axiom:Axiom_of_Extension/Set_Theory
}// axiom of extension ... axiom of extension axiom of extension
선택공리,choice_axiom axiom of choice, AoC
MKLINK
Zorn_lemma maybe 초른_보조정리,Zorn_lemma =,Zorn_lemma {
https://artofproblemsolving.com/wiki/index.php/Axiom_of_choice
https://encyclopediaofmath.org/wiki/Axiom_of_choice
선택공리
선택_공리
}// 선택공리 .... 선택공리
분리공리,separation_axiomZorn_lemma maybe 초른_보조정리,Zorn_lemma =,Zorn_lemma {
https://artofproblemsolving.com/wiki/index.php/Zorn's_Lemma
Zorn's_lemma = https://en.wikipedia.org/wiki/Zorn's_lemma
초른_보조정리 = https://ko.wikipedia.org/wiki/초른_보조정리
}
Banach-Tarski_paradox Banach-Tarski_paradox? =,Banach-Tarski_paradox . Banach-Tarski_paradoxZorn's_lemma = https://en.wikipedia.org/wiki/Zorn's_lemma
초른_보조정리 = https://ko.wikipedia.org/wiki/초른_보조정리
"부분순서집합,partially_ordered_set,poset이 극대원소,maximal_element를 가질 필요충분조건을 제시하는 lemma이며, 선택공리,choice_axiom와 동치이다."
ツォルンの補題 = https://ja.wikipedia.org/wiki/ツォルンの補題}
{
바나흐-타르스키 역설 ? 바나흐-타르스키 역설 바나흐-타르스키 역설
바나흐-타르스키 역설 ?
https://artofproblemsolving.com/wiki/index.php/Banach-Tarski_Paradox
역설,paradox?
}
axiom_of_choice = https://en.wiktionary.org/wiki/axiom_of_choice바나흐-타르스키 역설 ? 바나흐-타르스키 역설 바나흐-타르스키 역설
바나흐-타르스키 역설 ?
https://artofproblemsolving.com/wiki/index.php/Banach-Tarski_Paradox
역설,paradox?
}
https://artofproblemsolving.com/wiki/index.php/Axiom_of_choice
https://encyclopediaofmath.org/wiki/Axiom_of_choice
선택공리
선택_공리
}// 선택공리 .... 선택공리
{
axiom of separation
https://artofproblemsolving.com/wiki/index.php/Separation_axioms
https://ncatlab.org/nlab/show/axiom of separation
위상,topology 분리,separation 공리,axiom
}// axiom of separation .... axiom of separation axiom of separation axiom of separation axiom of separation
귀납공리,induction_axiom - 귀납,induction - curr at 귀납,inductionaxiom of separation
https://artofproblemsolving.com/wiki/index.php/Separation_axioms
https://ncatlab.org/nlab/show/axiom of separation
위상,topology 분리,separation 공리,axiom
}// axiom of separation .... axiom of separation axiom of separation axiom of separation axiom of separation
{
귀납,induction 공리,axiom
https://mathworld.wolfram.com/InductionAxiom.html
https://encyclopediaofmath.org/wiki/Induction_axiom
https://encyclopediaofmath.org/wiki/Induction_axiom
by 안드레이 콜모고로프 ?
probability axioms
수학백과: 공리적 확률에서 설명함.
확률,probability
probability_axiom
axiom_of_probability ?
axiom of probability ?
https://www.google.com/search?q=Axiom of probability
하면
Probability_axioms = https://en.wikipedia.org/wiki/Probability_axioms
} // 확률공리
probability_axiom
axiom_of_probability ?
axiom of probability ?
https://www.google.com/search?q=Axiom of probability
하면
Probability_axioms = https://en.wikipedia.org/wiki/Probability_axioms
} // 확률공리
countability_axiom =,countability_axiom =,countability_axiom . countability_axiom
{
가산성공리 ?
axiom of countability
axiom_of_countability
axiom_of_countability = https://en.wiktionary.org/wiki/axiom_of_countability x 2023-09-07
{
가산성공리 ?
axiom of countability
axiom_of_countability
axiom_of_countability = https://en.wiktionary.org/wiki/axiom_of_countability x 2023-09-07
mkl countability(curr . 가산집합)
Axiom_of_countability = https://en.wikipedia.org/wiki/Axiom_of_countability
Axiom_of_countability = https://en.wikipedia.org/wiki/Axiom_of_countability
ADDHERE........
공리관련 주제들 ¶
공리계,axiomatic_system ... 보다는 공리체계,axiomatic_system =,axiomatic_system 공리체계 axiomatic_system (KMS)
{
공리적 체계 ?
공리계
axiomatic
{
공리적 체계 ?
공리계
axiomatic
Sub:
categorical_axiomatic_system
페아노_공리계 Peano_axiomatic_system ? Peano_axioms ?
categorical_axiomatic_system
페아노_공리계 Peano_axiomatic_system ? Peano_axioms ?
MKLINK: 자연수,natural_number 자연수의 formal_definition 에 쓰임. see Natural_number#Formal_definitions
페아노_공리계 = https://ko.wikipedia.org/wiki/페아노_공리계
... Peano axioms
rel
페아노_공리,Peano_axiom
페아노_산술,Peano_arithmetic
Z공리계 ?페아노_공리계 = https://ko.wikipedia.org/wiki/페아노_공리계
... Peano axioms
rel
페아노_공리,Peano_axiom
페아노_산술,Peano_arithmetic
ZF공리계 ZF_axiomatic_system ?
NBG공리체계
MK공리체계
... zfc nbg mk
{
9개의 공리로 구성.
https://artofproblemsolving.com/wiki/index.php/Zermelo-Fraenkel_Axioms
Up: axiomatic_system
} ... zf axioms
ZFC공리계 ZFC_axiomatic_system ?9개의 공리로 구성.
https://artofproblemsolving.com/wiki/index.php/Zermelo-Fraenkel_Axioms
Up: axiomatic_system
} ... zf axioms
{
9개의 공리 + 선택공리,choice_axiom 해서 10개의 공리로 구성.
ZFC 공리계
https://ncatlab.org/nlab/show/ZFC
Up: axiomatic_system
} ... zfc axioms
NBG공리계9개의 공리 + 선택공리,choice_axiom 해서 10개의 공리로 구성.
ZFC 공리계
https://ncatlab.org/nlab/show/ZFC
Up: axiomatic_system
} ... zfc axioms
NBG공리체계
https://www.britannica.com/science/set-theory/The-Neumann-Bernays-Godel-axioms
...
폰 노이만-베르나이스-괴델(von Neumann-Bernays-Gödel)
nbg axioms
MK공리계...
폰 노이만-베르나이스-괴델(von Neumann-Bernays-Gödel)
nbg axioms
ZFC의 보존적 확장? chk // 보존적확장,conservative_extension =,conservative_extension . conservative_extension
{
conservative extension
opp. : non-conservative_extension { non-conservative extension } // non-conservative extension non-conservative extension
conservative_extension
https://ko.wikipedia.org/wiki/보존적_확장
https://en.wikipedia.org/wiki/Conservative_extension
https://ja.wikipedia.org/wiki/保存拡大
} // conservative extension conservative extension
conservative extension
opp. : non-conservative_extension { non-conservative extension } // non-conservative extension non-conservative extension
conservative_extension
https://ko.wikipedia.org/wiki/보존적_확장
https://en.wikipedia.org/wiki/Conservative_extension
https://ja.wikipedia.org/wiki/保存拡大
} // conservative extension conservative extension
MK공리체계
... zfc nbg mk
...
Twin
공리화,axiomatization
{
=공리화,axiomatization =,axiomatization . axiomatization 공리화
axiomatization
axiomatization = https://en.wiktionary.org/wiki/axiomatization
https://en.wikipedia.org/wiki/Axiomatic_system#Axiomatization
... Axiomatization Axiomatization
공리화 pagename due to axiomatization
}
{
=공리화,axiomatization =,axiomatization . axiomatization 공리화
axiomatization
axiomatization = https://en.wiktionary.org/wiki/axiomatization
https://en.wikipedia.org/wiki/Axiomatic_system#Axiomatization
... Axiomatization Axiomatization
공리화 pagename due to axiomatization
}
axiom_schema =,axiom_schema =,axiom_schema . axiom_schema (w)
aka axiom_scheme =,axiom_scheme =,axiom_scheme . axiom_scheme (via wt)
{
Twins:
https://foldoc.org/axiom schema
https://mathworld.wolfram.com/AxiomSchema.html
https://en.wikipedia.org/wiki/Axiom_schema
https://en.wikipedia.org/wiki/Axiom_schema
aka axiom_scheme =,axiom_scheme =,axiom_scheme . axiom_scheme (via wt)
{
Twins:
https://foldoc.org/axiom schema
https://mathworld.wolfram.com/AxiomSchema.html
https://en.wikipedia.org/wiki/Axiom_schema
https://en.wikipedia.org/wiki/Axiom_schema
Semi-twins:
https://planetmath.org/logicalaxiom 에서 "Any such a set of axioms is called an" 검색
… https://www.google.com/search?q=axiom schema
}
https://planetmath.org/logicalaxiom 에서 "Any such a set of axioms is called an" 검색
… https://www.google.com/search?q=axiom schema
}
....
공준,postulate이라는 용어도 있고 옛날엔 axiom과 구분했지만 요새는 별로 구분하지 않는다는 걸 본 기억이 있는데... 암튼 compare.
같은 단어 고유명사 액시엄,Axiom
{
Axiom Maths Program - Martin Baker
https://www.euclideanspace.com/prog/scratchpad/axiom/index.htm
{
Axiom Maths Program - Martin Baker
https://www.euclideanspace.com/prog/scratchpad/axiom/index.htm
}