Let X be a set and let A be a subset of X. Suppose there is an injection $f: X \rightarrow A$. Show that the cardinalities of A and X are equal.
The Attempt at a Solution
I tried proving this for hours but couldn't really get anywhere. So I was wondering if anybody could give me a hint so that I could start from there. By the way, I'm not supposed to use the Cantor-Bernstein Theorem.
Thanks in advance