ﾚｽ書き込み

純粋・応用数学・数学隣接分野（含むガロア理論）20

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

>>964
> >>949-950
> >補題１
> >　ωは任意の帰納的集合の共通部分である。
> 
> うむ
> １）その結論は、正しい。下記の独 de.wikipediaの英訳
> 　Infinity axiomで、”The natural numbers are therefore defined as the intersection of all inductive sets, as the smallest inductive set.”
> 　とある通りだ
> ２）ところで 下記の 独 de.wikipedia Infinity axiom では
> 　記号∩ 使ってないよ？
> 　記号∩ は、使わなくてもいいの？
> 　記号∩ は、使わなくてもいいのならば、その方がすっきりしてないかな？ｗ ；ｐ）
> 
> (参考)
> https://de.wikipedia.org/wiki/Unendlichkeitsaxiom
> （google翻訳 独→英）
> Infinity axiom
> The axiom of infinity is an axiom of set theory that postulates the existence of an inductive set . It is called the axiom of infinity because inductive sets are also infinite sets .
> 
> formulation
> There are a lot A, which is the empty set ∅ and with each element
> x∈A also the amount x∪{x}contains.
> ∃A:(∅∈A∧∀x:(x∈A⇒x∪{x}∈A))
> The infinity axiom does not merely postulate, as the name might suggest, the existence of any infinite set. It postulates the existence of an inductive set and thus, consequently, the existence of the set of natural numbers according to John von Neumann's model .
> 
> Significance for mathematics
> Natural numbers
> By the existence of at least one inductive set
> I together with the exclusion axiom, the existence of natural numbers as a set is also ensured:
> N:={x∈I∣∀z(z inductive ⟹ x∈z)}
> The natural numbers are therefore defined as the intersection of all inductive sets, as the smallest inductive set.
> 
> Infinite quantities
> Without the infinity axiom, ZF would only guarantee the existence of finite sets. No statements could be made about the existence of infinite sets. The infinity axiom, together with the power set axiom , ensures that there are also uncountable sets, such as the real numbers.

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 0.024s