What is wrong with this "proof" ? "theorem: " for every positive integer n, if x and y are positive integers with max(x, y) = n, then x = y. "basis step: " suppose that n=1. if max(x, y) = 1 and x and y are positive integers, we have x = 1 and y=1. "inductive step: " let k be a positive integer. assume that whenever max(x, y) = k and x and y are positive integers, then x = y. now let max(x, y) = k + 1, where x and y are positive integers. then max(x – 1, y – 1) = k, so by inductive hypothesis, x – 1 = y – 1. it follows that x = y, completing the inductive step.