공리,axiom

Difference between r1.41 and the current

@@ -1,3 +1,5 @@
#noindex
##=====공리,axiom =,axiom 공리 axiom
[[기하학,geometry]]의 5공리
1
2
@@ -8,6 +10,18 @@
5를 부정해도 consistent ? 이걸 부정하면 : [[비유클리드_기하학,non-Euclidean_geometry]]

= Sub =
[[확장공리,extension_axiom]]? [[확장,extension]]?
{
'''axiom of extension'''
AKA
'''axiom of extensionality''', and
'''axiom of extent'''[* https://proofwiki.org/wiki/Axiom:Axiom_of_Extension/Also_known_as]
 
Via https://proofwiki.org/wiki/Definition:Set_Equality#Axiom_of_Extension
Rel. [[집합,set]] [[집합론,set_theory]] [[집합상등,set_equality]]
https://proofwiki.org/wiki/Axiom:Axiom_of_Extension
https://proofwiki.org/wiki/Axiom:Axiom_of_Extension/Set_Theory
}// axiom of extension ... Bing:"axiom of extension" Ggl:"axiom of extension"
[[순서공리,order_axiom]] - 이미있는페이지 [[순서공리]] - axiom of order ? - rel. [[순서,order]]
[[선택공리,choice_axiom]] axiom of choice, AoC
MKLINK
@@ -32,10 +46,17 @@
https://encyclopediaofmath.org/wiki/Axiom_of_choice
[[Namu:선택공리]]
WpKo:선택_공리
}// 선택공리 .... NN:선택공리
 
[[분리공리,separation_axiom]]
{
'''axiom of separation'''

분리공리? separation_axiom
https://artofproblemsolving.com/wiki/index.php/Separation_axioms
[[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]]
{
@@ -138,18 +159,7 @@
[[WpKo:페아노_공리계]] = https://ko.wikipedia.org/wiki/페아노_공리계
... Google:Peano+axioms
rel
[[페아노_공리,Peano_axiom]] =페아노_공리,Peano_axiom =,Peano_axiom 페아노_공리 Peano_axiom
[[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
[[페아노_공리,Peano_axiom]]
[[페아노_산술,Peano_arithmetic]]

Z공리계 ?
@@ -254,7 +264,9 @@
= Twins =
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

[edit]

Sub

확장공리,extension_axiom? 확장,extension?
{
axiom of extension
AKA
axiom of extensionality, and
axiom of extent[1]

Via https://proofwiki.org/wiki/Definition:Set_Equality#Axiom_of_Extension
Rel. 집합,set 집합론,set_theory 집합상등,set_equality
https://proofwiki.org/wiki/Axiom:Axiom_of_Extension
https://proofwiki.org/wiki/Axiom:Axiom_of_Extension/Set_Theory
}// axiom of extension ... Bing:axiom of extension Ggl:axiom of extension
순서공리,order_axiom - 이미있는페이지 순서공리 - axiom of order ? - rel. 순서,order
선택공리,choice_axiom axiom of choice, AoC
MKLINK
Zorn_lemma maybe 초른_보조정리,Zorn_lemma =,Zorn_lemma {
https://artofproblemsolving.com/wiki/index.php/Zorn's_Lemma
WpEn:Zorn's_lemma = https://en.wikipedia.org/wiki/Zorn's_lemma
WpKo: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."
WpJa:ツォルンの補題 = https://ja.wikipedia.org/wiki/ツォルンの補題
}
Banach-Tarski_paradox Banach-Tarski_paradox? =,Banach-Tarski_paradox . Banach-Tarski_paradox
{
바나흐-타르스키 역설 ? Ggl:바나흐-타르스키 역설 Ndict:바나흐-타르스키 역설
바나흐-타르스키 역설 ?
https://artofproblemsolving.com/wiki/index.php/Banach-Tarski_Paradox
역설,paradox?
}

WtEn:axiom_of_choice = https://en.wiktionary.org/wiki/axiom_of_choice

https://artofproblemsolving.com/wiki/index.php/Axiom_of_choice
https://encyclopediaofmath.org/wiki/Axiom_of_choice
Namu:선택공리
WpKo:선택_공리
}// 선택공리 .... NN:선택공리

분리공리,separation_axiom
{
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 .... 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
{
귀납,induction 공리,axiom




completeness_axiom =,completeness_axiom =,completeness_axiom . completeness_axiom
{
완비성공리 ?



확률공리 =,probability_axiom =,probability_axiom . probability_axiom
{

by 안드레이 콜모고로프 ?

probability axioms





Ggl:확률공리
Ggl:probability axioms
확률공리
"probability axioms"
}

Playfair_axiom =,Playfair_axiom =,Playfair_axiom . Playfair_axiom
{
geometry에서 parallel_postulate관련


확률공리,probability_axiom =확률공리,probability_axiom =,probability_axiom 확률공리 probability_axiom
{
확률공리

확률,probability
probability_axiom
axiom_of_probability ?
axiom of probability ?
https://www.google.com/search?q=Axiom of probability
하면
WpEn: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
WtEn:axiom_of_countability = https://en.wiktionary.org/wiki/axiom_of_countability x 2023-09-07


Ggl:axiom of countability
Naver:axiom of countability
"axiom of countability"
}

ADDHERE........

[edit]

공리관련 주제들

공리계,axiomatic_system ... 보다는 공리체계,axiomatic_system =,axiomatic_system 공리체계 axiomatic_system (KMS)
{
공리적 체계 ?
KmsK:공리계
KmsE:axiomatic

Sub:
categorical_axiomatic_system
categorical axiomatic system
https://mathworld.wolfram.com/CategoricalAxiomaticSystem.html
페아노_공리계 Peano_axiomatic_system ? Peano_axioms ?
MKLINK: 자연수,natural_number 자연수의 formal_definition 에 쓰임. see WpEn:Natural_number#Formal_definitions
WpKo:페아노_공리계 = https://ko.wikipedia.org/wiki/페아노_공리계
... Google:Peano axioms
rel
페아노_공리,Peano_axiom
페아노_산술,Peano_arithmetic

Z공리계 ?

ZF공리계 ZF_axiomatic_system ?
{
9개의 공리로 구성.
https://artofproblemsolving.com/wiki/index.php/Zermelo-Fraenkel_Axioms
Up: axiomatic_system
} ... Google:zf axioms

ZFC공리계 ZFC_axiomatic_system ?
{
9개의 공리 + 선택공리,choice_axiom 해서 10개의 공리로 구성.
Namu:ZFC 공리계
https://ncatlab.org/nlab/show/ZFC
Up: axiomatic_system
} ... Google:zfc axioms

NBG공리계
NBG공리체계
https://www.britannica.com/science/set-theory/The-Neumann-Bernays-Godel-axioms
...
Ggl:폰 노이만-베르나이스-괴델(von Neumann-Bernays-Gödel)
Google: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 Ggl:non-conservative extension

WtEn: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
'보존확대'.
Namu:拡 Naver:拡은 擴 의 약자.... Namu:擴 -> 넓힐 확. 확대할때 그거..

} // conservative extension Ggl:conservative extension

MK공리계
MK공리체계
Ggl:모스-켈리(Morse-Kelley) 공리계


... Google:zfc nbg mk

...


Twin









....

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

}

[edit]

Twins

----
공리,axiom Modified on 10:31 pm, July 10, 2024.
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