Cantor's theorem: Difference between revisions

Revision as of 03:14, 24 June 2004

Revision as of 03:15, 24 June 2004

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[[Category:Set theory]]

In [[set theory]], '''Cantor's theorem''' states that the [[power set]] ([[set]] of all [[subset]]s) of any set ''A'' has a strictly greater [[cardinality]] than that of ''A''. Cantor's Theoremtheorem is obvious for finite sets, but surprisingly it holds true for infinite sets as well. In particular, the [[power set]] of a [[countable set|countably infinite]] set is '''un'''countably infinite. To illustrate the validity of Cantor's Theorem for infinite sets, just test an infinite set in the proof below.

==The proof==