Quandaries and Queries


Hi, my name's David and I'm in college in York, PA.
I've been to your site and am interested on the subject of division by 0. It's easy enough to give answers, but it's very hard, especially in this case, to make someone understand a mathematical problem.
It's been about a year since my Calc class, and we never went over division by 0, only infinite numbers and such. My question is: How would you work a problem of (real number) / 0? As ignorant as it may sound to you, I am having trouble grasping this since I've only begun to understand some of it. Perhaps you could help.


Hi David,

Think of division as the inverse operation to multiplication. That is I want to think of

a b = c


a = c/b

as equivalent satements.

This is certainly true if b is not zero, but what if b = 0? There are two cases to consider.

Case 1: c is not zero.

The first equation is then a 0 = c where c is not zero. Clearly there is no such number a, since for every number a, a  0 = 0. Thus if c is not zero, then  c/0 is not a number.

Case 2: c = 0

The first equation is then a 0 = 0. In this case a can be any number and a 0 = 0 is true. Thus  0/0 might be any number. Not a happy prospect, not knowing what number 0/0 is. The usual way that mathematicians deal with this problem is to say that 0/0 is not a number.

The answer to your question of "How would you work a problem of (real number) / 0?" is to say that division by zero is not allowed.



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