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HomeCantor's theorem

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Related:

CantorsDiagonalArgument, KonigsTheorem

Type of Math Object:

Theorem

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Reference

## Mathematics Subject Classification

03E17*no label found*03E10

*no label found*

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## Comments

## Power set of naturals

Let N2 be the set of even numbers. According to Cantor, you can’t establish a bijection between N2 and it’s power set, P(N2). Consider anyway that correspondence, take any not-counted subsets of P(N2) and put them in correspondence with odd numbers. This way, Cantor fails to prove that P(N2) is uncountable.

## power set of naturals

You can’t put the power set in 1-1 correspondence with odd numbers either.

## No, but you can with both

No, but you can with both even and odds. Actually, Cantor didn’t proved you can’t, because the correspondence between N and P(N2) is not covered by his argumentation.