Do Infinite Sets K Have Equal Cardinalities for Permutations and All Functions?

moo5003 · Apr 18, 2008

Is it true that the set of permutations on a infinite set K has the same cardinality as all functions between a infinite set K to itself?

Pere Callahan · Apr 18, 2008

Did you try to set up a bijection? Or did you try anything to (dis)prove what you're aksing for?

HallsofIvy · Apr 19, 2008

To add to what Pere Callahan said: How many permutations are there on K= {a, b}?
How many functions are there from K to K?
(Permutations are one-to-one and onto functions.)

Do Infinite Sets K Have Equal Cardinalities for Permutations and All Functions?

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Do Infinite Sets K Have Equal Cardinalities for Permutations and All Functions?

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