Suppose that {An : n e N} is a family of sets (not necessarily pairwise disjoint) such that An is countable for every n. Prove that UnEN An is countable. (Hint: prove that there is a surjection f : N...

4

Extracted text: Suppose that {An : n e N} is a family of sets (not necessarily pairwise disjoint) such that An is countable for every n. Prove that UnEN An is countable. (Hint: prove that there is a surjection f : N x N → Unen An and say why this is sufficient.)