Exercise 1.5.1. Finish the following proof for Theorem 1.5.7. Assume B is a countable set. Thus, there exists f : N → B, which is 1–1 and onto. Let A ⊆ B be an infinite subset of B. We must show that A is countable. Let n1 = min{n ∈ N : f(n) ∈ A}. As a start to a definition of g : N → A, set g(1) = f(n1). Show how to inductively continue this process to produce a 1–1 function g from N onto A.