Cardinality of Functions

  • Thread starter moo5003
  • Start date
207
0

Main Question or Discussion Point

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?
 

Answers and Replies

Did you try to set up a bijection? Or did you try anything to (dis)prove what you're aksing for?
 
HallsofIvy
Science Advisor
Homework Helper
41,734
893
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.)
 

Related Threads for: Cardinality of Functions

  • Last Post
Replies
9
Views
3K
Replies
14
Views
9K
Replies
6
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
6
Views
3K
Replies
4
Views
3K
  • Last Post
Replies
10
Views
10K
Top