1. The problem statement, all variables and given/known data Prove that if A and B are denumerable sets, not necessarily disjoint, then AUB is denumerable. 2. Relevant equations 3. The attempt at a solution So I started my saying that since A and B are denumerable then, f:N-->A and g:N-->B are bijections. The I defined h(n) in terms of f and g as such: h(n) = f(n/2) if n is even h(n) = g((n+1)/2) if n is odd This is all I have so far. I am not sure where to go or what this tells me.