1. The problem statement, all variables and given/known data Suppose that A and B are both countably infinite sets. Prove that there is a one to one correspondence between A and B. 2. Relevant equations 3. The attempt at a solution By definition of countably infinite, there is a one to one correspondence between Z+ and A and Z+ and B. Let n ε Z+. All elements of A and B can be listed as follows A = a1, a2, a3, ... , an B = b1, b2, b3, ... , bn I was going to say that if f(n) = an and f(n) = bn, then an = bn, but f:Z -> A by x and f: Z -> B by x^2 makes this invalid. I know that because A and B are both countably infinite, they are cardinally equivalent, and that if they are cardinally equivalent, then there exists a one to one correspondence between the two sets, but I can't seem to get the proof.