ﾚｽ書き込み

ガロア第一論文と乗数イデアル他関連資料スレ13

PC,ｽﾏﾎ,PHSは ULA べっかんこ公式(ｽﾏﾎ) 公式(PC) で書き込んでください｡

名前
ﾒｰﾙ
引用切替：ﾚｽｱﾝｶｰのみ

>>367
> >>360
> >>順序数全体の集まりは集合でない。
> >順序数全体のクラスOを集合と仮定する。
> >このときOも順序数だからO∈O。正則性公理に反するから仮定は偽、すなわちOは集合でない。
> 
> アホなおサルと>>7-10、 10分議論をする暇があったら
> 下記のen.wikipedia Ordinal number を、3分黙読する方が、よほど有益だわｗ ；ｐ）
> （日wikipediaには、順序数のクラスの記述はないけどね （＾＾）
> 
> (参考)
> https://ja.wikipedia.org/wiki/%E9%A0%86%E5%BA%8F%E6%95%B0
> 順序数（じゅんじょすう、英: ordinal number）とは、整列集合同士の“長さ”を比較するために、自然数[1]を拡張させた概念である。
> 
> https://en.wikipedia.org/wiki/Ordinal_number
> Ordinal number
> In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite sets.[1]
> 
> Definitions
> Well-ordered sets
> Essentially, an ordinal is intended to be defined as an isomorphism class of well-ordered sets: that is, as an equivalence class for the equivalence relation of "being order-isomorphic". There is a technical difficulty involved, however, in the fact that the equivalence class is too large to be a set in the usual Zermelo–Fraenkel (ZF) formalization of set theory. But this is not a serious difficulty. The ordinal can be said to be the order type of any set in the class.
> 
> Definition of an ordinal as an equivalence class
> The original definition of ordinal numbers, found for example in the Principia Mathematica, defines the order type of a well-ordering as the set of all well-orderings similar (order-isomorphic) to that well-ordering: in other words, an ordinal number is genuinely an equivalence class of well-ordered sets. This definition must be abandoned in ZF and related systems of axiomatic set theory because these equivalence classes are too large to form a set. However, this definition still can be used in type theory and in Quine's axiomatic set theory New Foundations and related systems (where it affords a rather surprising alternative solution to the Burali-Forti paradox of the largest ordinal).
> 
> Von Neumann definition of ordinals
> See also: Set-theoretic definition of natural numbers and Zermelo ordinals
> Rather than defining an ordinal as an equivalence class of well-ordered sets, it will be defined as a particular well-ordered set that (canonically) represents the class. Thus, an ordinal number will be a well-ordered set; and every well-ordered set will be order-isomorphic to exactly one ordinal number.

ﾛｰｶﾙﾙｰﾙ SETTING.TXT

他の携帯ﾌﾞﾗｳｻﾞのﾚｽ書き込みﾌｫｰﾑはこちら｡書き込み設定で書き込みｻｲﾄの設定ができます｡
・ULA
・べっかんこ(身代わりの術)
・べっかんこ(通常)
・公式(ｽﾏﾎ)
・公式(PC)[PC,ｽﾏﾎ,PHS可]

書き込み設定(板別)で板別の名前とﾒｰﾙを設定できます｡

上下板覧索設栞歴

ぬこの手ぬこTOP 0.011s