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現代数学の系譜　カントル　超限集合論

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引用切替：ﾚｽｱﾝｶｰのみ
>>541 > >>540 > つづき > > ?As we know, the set of all objects (if it exists) enjoys paradoxical properties: unlike a theorem known to G. Cantor, the power of this set would not be inferior to that of the class of all its subassemblies. > It is the same of the class composed of all the sets > containing a single element; therefore, K classes do not check, Cantor's theorem. > ?Taking this fact into account, one could question the very existence of classes K. > > By modifying Mr. Sierpinski's definition so as to remove that drawback, I get the following definition: > > The set M is finite, when the class of all its subsets > (not empty) is the only class satisfying the conditions: > 1. its elements are subsets (not empty) of M; > 2. any set containing a single element of M belongs to this class; > 3. if A and B are two sets belonging to this class, their set -sorn A + B also belongs to it. > > つづく
ﾛｰｶﾙﾙｰﾙ SETTING.TXT

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