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現代数学の系譜　カントル　超限集合論

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>>508 > >>504 追加 > > https://en.wikipedia.org/wiki/Finite_set > Finite set > (抜粋) > > Necessary and sufficient conditions for finiteness > In Zermelo?Fraenkel set theory without the axiom of choice (ZF), the following conditions are all equivalent:[citation needed] > > 2.(Kazimierz Kuratowski) S has all properties which can be proved by mathematical induction beginning with the empty set and adding one new element at a time. (See below for the set-theoretical formulation of Kuratowski finiteness.) > > Set-theoretic definitions of finiteness > > Various properties that single out the finite sets among all sets in the theory ZFC turn out logically inequivalent in weaker systems such as ZF or intuitionistic set theories. > Two definitions feature prominently in the literature, one due to Richard Dedekind, the other to Kazimierz Kuratowski. (Kuratowski's is the definition used above.) > > つづく
ﾛｰｶﾙﾙｰﾙ SETTING.TXT

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