Identify the mistakes, if any, with the following “proof” by…
Identify the mistakes, if any, with the following “proof” by strong induction. “Theorem” For every nonnegative integer n, 5n = 0. Basis Step: 5 ⋅ 0 = 0. Inductive Step: Suppose that 5j = 0 for all nonnegative integers j with 0 ≤ j ≤ k. Write k + 1 = i + j, where i and j are natural numbers less than k + 1. By the inductive hypothesis, 5(k + 1) = 5(i + j) = 5i + 5j = 0 + 0 = 0.