19/10/05 21:35:51.26 JrhjRl4x.net
>>91 補足
”The natural numbers are represented by Zermelo as by Φ, {Φ}, {{Φ}}, …, and the Axiom of Infinity gives us a set of these.
Moreover, it seems that, since both the set of natural numbers and the power set axiom are available, there are enough sets to represent the rationals and the reals, functions on reals etc.
What are missing, though, are the details: how exactly does one represent the right equivalence classes, sequences etc.?”
ツェルメロ自然数構成
批判はされているけれど（＾＾
・by Φ, {Φ}, {{Φ}}, …, and the Axiom of Infinity gives us a set of these
・since both the set of natural numbers and the power set axiom are available, there are enough sets to represent the rationals and the reals, functions on reals etc.
・何が不足なの？ What are missing, though, are the details: how exactly does one represent the right equivalence classes, sequences etc.?
まあ、ツェルメロ自然数構成から、無限集合が出来て、自然数とその冪集合から、有理数や実数や実関数などはできる
でも、批判はあった。それは、基礎論パイオニアの宿命でもあったかもしれない（＾＾