[過去ﾛｸﾞ] 現代数学の系譜　カントル　超限集合論 (1002ﾚｽ)
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542(1): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2019/11/30(土)20:55 ID:4Ujjq2jv(7/17) AAS
>>541
つづき

?We can show that a finite set according to this definition is also in the ordinary sense and reciprocally.
In other words: for a set to be finite according to the proposed definition, it is necessary and sufficient that the number of its elements can be expressed by a natural number (the notion of natural number being assumed to be known).
?Indeed, let M be a set whose number of elements can be expressed by a natural number; let Z be any class satisfying the conditions 1-3.
We will show that every subset of M belongs to Z.
This is - under condition 2 - subsets composed of a single element; at the same time, if this is so subsets containing n elements, it is the same - according to 3 - of those which contain n + 1.
省8

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543: 現代数学の系譜 雑談 ◆e.a0E5TtKE 2019/11/30(土)21:00 ID:4Ujjq2jv(8/17) AAS
>>542 補足

?We can show that a finite set according to this definition is also in the ordinary sense and reciprocally.
　↑
？は、先頭のブランクが、文字化けしているんだ
Google翻訳の仕様なのでしょうね
目で見ると、ブランクで通常と変わりないが、５CH板に貼ると化けるんだ（＾＾；

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