February 25, 2017

Homework Help: Discrete Math

Posted by Francesca on Friday, March 25, 2011 at 9:22pm.

Theorem: For every integer n, if x and y are positive integers with max(x, y) = n, then x = y.
Basic 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.

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