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Theorem 16.11 Let A be a set. The set A is infinite if and only if...

Theorem 16.11 Let A be a set. The set A is infinite if and only if there is a proper subset B of A
for which there exists a 1–1 correspondence f : A -> B.

Complete the proof of Theorem 16.11 as follows: Begin by assuming that A is infinite.
Let a1, a2,... be an infinite sequence of distinct elements of A. (How do we know such a sequence
exists?) Prove that there is a 1–1 correspondence between the set A and the set B = A\{a1}.

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