Injection - Bijection function Question Suppose $A, B$ are two non-empty sets and let $$f:A\to B$$ and $$g:B\to A$$ be two injective (one to one) functions.
QUESTIONS:
1. Is there exist a bijective function from $A$ to $B$?
2. If so, how can we prove it?  
I think, there should be a such function. But I can not come up with an argument to prove it?

Yes. Such a bijection must exists. This is the topic of the Cantor–Bernstein theorem.
