I have the following question:
Prove that a set A has the same cardinality of a subset of a Set B, if and only if exists an injective function A to B.
I find it hard to prove it because I can easily find a set A which is:
C is a subset of B. C's cardinality is bigger than A's.
There is an injective function from A to B, of course.
where am I wrong?