proof of Cantor's theorem

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Keywords:
diagonal argument
Major Section:
Reference
Type of Math Object:
Proof

Mathematics Subject Classification

infinite sets

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.