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Possible Duplicate:
power set cardinal equality

Let $X$ and $Y$ be sets, and suppose that $|\mathscr{P}(X)| = |\mathscr{P}(Y)|$ (where $\mathscr{P}$ denotes the power set).

Does it follow that $|X|=|Y|$?

Remark: It's obviously true for finite sets, as $2^m=2^n$ implies $m=n$.

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    For all $A$, $|P(A)|=2^{|A|}$.2012-05-10
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    @SalechAlhasov: How is that useful here?2012-05-10
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    @ChrisEagle: I really don't know. In future, I'll try to avoid with such comments.2012-05-10
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    Thanks for pointing out the previous question.2012-05-10

1 Answers 1