2.5.3 What is wrong with the following proof? Explain why this error could be prevented by plan-

ning out a proof before writing it.

Theorem 2.40. If n ≥ 3 is an integer, then n² > 2n + 1.

Proof. Let n² > 2n + 1. Then 0 < n² - 2n − 1 = (n − 1)² -2, which is only true when n > 3.

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