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.