Apr 18, 2008 #1 moo5003 Messages 202 Reaction score 0 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?
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?
Apr 18, 2008 #2 Pere Callahan Messages 582 Reaction score 1 Did you try to set up a bijection? Or did you try anything to (dis)prove what you're aksing for?
Apr 19, 2008 #3 HallsofIvy Science Advisor Homework Helper Messages 42,895 Reaction score 983 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.)
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.)