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proof of Cantor's theorem

diagonal argument
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Mathematics Subject Classification

03E17 no label found03E10 no label found


You proved that |P(X)| is bigger than |X|, because you can't find any x so that F(x)=Z.
But what does it means for infinite sets |P(X)|=|X|+1 ?
It's like saying that natural numbers are more numerous than even numbers. You're right, but they have the same cardinal.

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