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In mathematical [[set theory]], '''Cantor's theorem''' is a fundamental result which states that, for any [[Set (mathematics)|set]] <math>A</math>, the set of all [[subset]]s of <math>A,</math> known as the [[power set]] of <math>A,</math> has a strictly greater [[cardinality]] than <math>A</math> itself.
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For [[finite set]]s, Cantor's theorem can be seen to be true by simple [[enumeration]] of the number of subsets. Counting the [[empty set]] as a subset, a set with <math>n</math> elements has a total of <math>2^n</math> subsets, and the theorem holds because <math>2^n > n</math> for all [[non-negative integers]].
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