Cardinality: Let A and B be sets. We write A B (and say A has the same cardinality as B) if there is bijection f : A B. We write A < B if there is an injection f : A -→ B. Theorem 1: Let A and B be sets. Then, A B if and only if A < B and B< A. Exercise 2: Let neZ and suppose n > 1. Use Theorem 1 to prove or disprove that N N".

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A: This is a problem of Real Analysis and Topology.

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A: We will solve the problem.

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