The first step is to note that because we know there exists injective maps and so is injective. Which means . Now you argue that it is not possible to have . Assume that if is bijection. Then is a bijection contradicting the fact that .

This is not a good set. is a set of all function from to where?2. Let K be any set, and let F be the set of all functions with domain K. Then card K < card F.