- #1
bobby2k
- 127
- 2
Homework Statement
Let K be any set and let F* be the set of all functions with domain K. Prove that card K < card F*.
The Attempt at a Solution
I am first able to show that card K <= card F*, by creating an invertible function from K into F*.
let f: K -> F*
be defined so that if k is an element of K, then f(k) = {(i,k): i is an element of K}.
Basically we create a function with function value of k in all points.
But this only shows <= , I am not sure of to prove <. Then I think I must assume that there is a bijection, but that this leads to a contradiction. How do I do that?