Mathematical induction can be used not only to prove equalities, but also to prove inequalities. The predicate P(n) is the statement n! < n" where n is an integer greater than 1. a) What is the statement P(2)? b) Show that P(2) is true, i.e., complete the basis step of the proof by induction. c) What is the inductive hypothesis of a proof by mathematical induction that P(n) is true for all natural numbers n greater than 1? Recall that n! is the factorial of n, i.e., n! = 1 ·2·3... (n – 1) · n.

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