Department of Mathematics --- College of Science --- University of Utah

Mathematics 1010 online

Never Divide by Zero

Division by zero is undefined, and for good reason. If we assigned a number to the result of dividing by zero we'd run into contradictions, and mathematics would become useless.

Let's approach the issue from several angles:

The Moral of the Story

Whenever you divide by anything you should think about the possibility of the divisor being zero. This should become a reflex like checking your blind spot when you change lanes on the freeway. Usually there is no problem, but if in fact there is somebody in your blind spot then the consequences can be devastating, and you want to avoid the resulting carnage!

The Answer to the Puzzle

In going from (3) to (4) we divide by zero since $ (*)$ implies that $ a-b=0$.