1. The problem statement, all variables and given/known data Suppose A and B are both countably infinite sets. Prove there is a 1-1 correspondence between A and B. 2. Relevant equations 3. The attempt at a solution Since A is countably infinite, there exists a mapping f such that f maps ℕto A that is 1-1 and onto. Similarly for B, there exists a mapping g such that g maps ℕto B that is 1-1 and onto. Since g is 1-1 and onto, g^-1 exists and g^-1 maps B into ℕ Hence g^-1(b)=n for all b in B. Since f(n)=a for all n in ℕ, then f(g^-1(b))=a for all b in B since g^-1(b) yields its corresponding number from ℕ. Since f and g are bijective, we can define h as a mapping from B to A by h(b)=a for all b in B by using the ordering created by the mapping g. Does this make sense?