So if I have two sets A and B and if |A| = |B| and if function f is a function from A to B and is injective, how can I prove that it is also surjective?

Forgot to mention. A and B are finite sets.

  • $\begingroup$ Think about the map $f:\mathbb N\to\mathbb N$ where $$f(x)=x+1$$It's injective but not surjective. The claim is only true if $|A|<\infty$. $\endgroup$ – Don Thousand Nov 6 at 5:58
  • $\begingroup$ See this or this. $\endgroup$ – Don Thousand Nov 6 at 6:00