1. The problem statement, all variables and given/known data 2. Relevant equations Countable Infinite is defined if X is infinite and X is isomorphic to the Natural Numbers. 3. The attempt at a solution Now I assume that XUY is isomorphic to the Natural Numbers. So X ∪ Y ≅ N . Now here's where I get confused. I am unsure how to define a function that is invertible (to prove the bijection of being 1-1 and onto). Does anyone have an idea on where to go with this proof? Thank you, G.