De ne function f : Z ! N by f(n) = 2n if n > 0 and f(n) = 1 ? 2n if n   0. (a) Observe that the positive integers in Z are mapped to even numbers and all other integers in Z are mapped to odd numbers. Prove that f is a bijection. (b) Recall that N is a countable set (these are the counting numbers). Does part (a) imply that Z is also countable? Explain.

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