I've been stumped on this stupid question for 3 days, guys. I have to locate the flaw in this proof. I have no clue what's wrong with it. According to the rules of inductive reasoning, it works

'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.