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A division by zero is primarily an algebraic question. The reasoning therefore follows the indirect pattern of most algebraic proofs:

What if it was allowed?

Then we would get a contradiction, and a contradiction is the greatest enemy of mathematical rigor. Many students tried to find a way to divide by zero once in their lifetime. To be honest: It is possible! We could allow it! However, that would come at a price. We had to give up other laws which we did not want to lose; most of all the fact that ##0## and ##1## are two different numbers. A division by zero often results in the equation ##1=0## which would make both of them pretty useless. But it also causes problems for other, often unexpected rules and laws that we do not want to give up.

Why division by zero is a bad idea as it implies …

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