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edited Apr 13, 2017 at 12:58

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Cardinality of the permutations of an infinite set Cardinality of the permutations of an infinite set

Why does the symmetric group on an infinite set X have the cardinality of the power set ${\cal P}(X)$?

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edited Jul 19, 2010 at 14:38

Possible Duplicate:
Cardinality of the permutations of an infinite set

Why does the symmetric group on an infinite set X have the cardinality of the power set ${\cal P}(X)$?

Post Closed as "exact duplicate" by Steve Huntsman, Gjergji Zaimi, Robin Chapman, Martin Brandenburg, Kim Morrison

occurred Jul 19, 2010 at 14:38

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asked Jul 19, 2010 at 13:35

Cardinality of symmetric group

Why does the symmetric group on an infinite set X have the cardinality of the power set ${\cal P}(X)$?

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