Cantor's paradox


Cantor's paradox
The contradiction arising if we compare for size the set of all sets, and its own power set . By Cantor's theorem the power set must be bigger (contain more members). But it is itself a subset of the set of all sets, and so cannot be bigger. The paradox shows that the collection of all sets cannot itself be a set-theoretic object.

Philosophy dictionary. . 2011.

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