Question

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 the inductive hypothesis, x – 1 = y – 1. It follows that x = y, completing the inductive step. Online Discussion Guidelines: Post your logical argument on the discussion forum. Read the logical argument of your peers. Reply the results posted by at least two of your peers.

Answer 1

The assumption of the inductive step is not correct. If $\mathrm{max}(x,y)=2$, for instance, it's entirely possible that $x=1$ and $y=2$.