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

기하학,geometry의 5공리
1
2
3
4 까지는 유클리드_기하학,Euclidean_geometry과 공통이지만
5 평행선공준,parallel_postulate

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 ...

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

Zorn'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
}

Banach-Tarski_paradox Banach-Tarski_paradox? =,Banach-Tarski_paradox . Banach-Tarski_paradox

{
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_choice

https://artofproblemsolving.com/wiki/index.php/Axiom_of_choice
https://encyclopediaofmath.org/wiki/Axiom_of_choice

선택공리

선택_공리

분리공리? separation_axiom

https://artofproblemsolving.com/wiki/index.php/Separation_axioms
위상,topology separation 공리,axiom

귀납공리,induction_axiom - 귀납,induction - curr at

귀납,induction
{
귀납,induction 공리,axiom

귀납,induction -

귀납,induction
수학적귀납법,mathematical_induction -

수학적귀납법,mathematical_induction

https://mathworld.wolfram.com/InductionAxiom.html
https://encyclopediaofmath.org/wiki/Induction_axiom

...

귀납공리

귀납공리
}

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

실수,real_number
완비성,completeness

completeness_axiom
...

completeness.axiom

completeness axiom

완비성공리

완비성공리
}

확률공리 =,probability_axiom =,probability_axiom . probability_axiom
{

by 안드레이 콜모고로프 ?

probability axioms

확률,probability

수학백과: 공리적 확률에서 설명함.

https://en.wikipedia.org/wiki/Probability_axioms

확률공리

probability axioms
확률공리
"probability axioms"
}

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

Playfair's_axiom

playfair axiom
}

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

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

mkl countability(curr . 가산집합)

가산성,countability ? https://en.wiktionary.org/wiki/countability

rel 가산집합,countable_set

Axiom_of_countability = https://en.wikipedia.org/wiki/Axiom_of_countability

axiom of countability

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 ?

공리계

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

Natural_number#Formal_definitions

페아노_공리계 = https://ko.wikipedia.org/wiki/페아노_공리계
...

Peano axioms
rel
페아노_공리,Peano_axiom =페아노_공리,Peano_axiom =,Peano_axiom 페아노_공리 Peano_axiom

Natural_number#Peano_axioms

Peano_axioms
= https://en.wikipedia.org/wiki/Peano_axioms

ペアノの公理
https://ja.wikipedia.org/wiki/ペアノの公理
...
"페아노 공리"

페아노 공리

rel
페아노_산술,Peano_arithmetic

Z공리계 ?

ZF공리계 ZF_axiomatic_system ?

{
9개의 공리로 구성.
https://artofproblemsolving.com/wiki/index.php/Zermelo-Fraenkel_Axioms
Up: axiomatic_system
} ...

zf axioms

ZFC공리계 ZFC_axiomatic_system ?

{
9개의 공리 + 선택공리,choice_axiom 해서 10개의 공리로 구성.

ZFC 공리계
https://ncatlab.org/nlab/show/ZFC
Up: axiomatic_system
} ...

zfc axioms

NBG공리계
NBG공리체계

https://www.britannica.com/science/set-theory/The-Neumann-Bernays-Godel-axioms
...

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

'보존확대'.

拡

拡은 擴 의 약자....

擴 -> 넓힐 확. 확대할때 그거..

} // conservative extension

conservative extension

MK공리계
MK공리체계

모스-켈리(Morse-Kelley) 공리계

...

zfc nbg mk

...

Twin

AxiomaticSystem
= https://mathworld.wolfram.com/AxiomaticSystem.html

https://www.gabormelli.com/RKB/Axiomatic_System

Up: 공리,axiom system

...

공리계

axiomatic_system
} // axiomatic system

axiomatic system

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
}

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

Semi-twins:
https://planetmath.org/logicalaxiom 에서 "Any such a set of axioms is called an" 검색

... 하이라이트 링크 : https://planetmath.org/logicalaxiom#:~:text=Any such a set of axioms is called

… https://www.google.com/search?q=axiom schema
}

axiomatic_set_theory

....

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 ¶

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

----

[1] https://proofwiki.org/wiki/Axiom:Axiom_of_Extension/Also_known_as

Red Ruby Wiki

minus(U+2212): −
asymp equal(U+2243): ≃

공리,axiom

Difference between r1.41 and the current

Sub ¶

공리관련 주제들 ¶

Twins ¶