Q&A #3893

Teachers' Lounge Discussion: Dividing by zero

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From: Ralph Ades

To: Teacher2Teacher Public Discussion
Date: 2004091022:33:52
Subject: Re: Dividing by zero

I just stumbled upon this website and hence this topic. Here is a proof of the impossibility of dividing by zero. Suppose that you can divide by zero and let 'a' be a nonzero integer such that a/0 = 0. This implies that 0 * 0 = a, which is true only if a equals 0. This contradicts our assumption that 'a' is nonzero. That kills the first part of the proof. Now suppose 0/0 = a, where 'a' is an integer. This implies that a*0=0, which is true. I claim that 0/0=b ,where 'b' is an integer different from 'a', is also true since the equality b*0=0 holds. This implies that 0/0=a=b, which contradicts the assumption that 'a' and 'b' are not equal(6/2 = 3 and no other number. In otherwords, this binary operation is not well defined for division by 0). Uniqueness fails and hence one cannot divide by zero.

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