Hello,

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:

A={1,2}

B={1,2,3,4}

C={1,2,3}

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?

Thank you!