1. The problem statement, all variables and given/known data Without using the Axiom of Choice, show that if A is a well-ordered set and f : A -> B is a surjection to any set B then there exists an injection B -> A. 2. Relevant equations 3. The attempt at a solution I was wondering if the existence of the surjection from a well ordered set A implies that B is well ordered, and if so how would I prove this? Is this even the right way to start? I'm pretty lost on this so any starting hints would be appreciated.