Date: May 6, 1999 1:04 AM
Author: Brian Harvey
Subject: Re: lovely proof problem
Anonymous writes:

>This is a problem I got for my computer science-discrete math class:

>

>Prove or disprove that the product of a nonzero rational number and an

>irrational number is irrational using one of the following: direct proof

>(of the form p --> q), indirect proof (of the form ~q --> ~p), proof by

>contradiction (so that ~p --> q is true, then ~p must be false, so p must be

>true).

What does this have to do with discrete math?

(Perhaps it's just that nobody learns what a proof is in their

non-discrete math classes any more?)

Anyway, which proof techniques can be used depends a lot on what theorems

we already have available. Since the definition of an irrational number

is based on a property it DOESN'T have, I'm betting that any proof will

turn out to involve some use of proof by contradiction somewhere along

the line, although that might be hidden in the proof of a previous theorem.

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