CyberVenice

I wondered about dividing by zero for years.

True story
In 2nd grade, the teacher said to the class, "you can't divide by zero". I put my hand and said, "Okay, I won't, but what if you *did* divide by zero, what would happen?" And the teacher said, "well, you just can't divide by zero."

So five minutes later, I raised my hand, and said, "yeah, but WHAT IF you did divide by zero? What would you get?". And the teacher said, "well, you just can't divide by zero and that's that."

So five minutes go by, and I raise my hand and say, "Okay, but what would happen if you did divide by zero?". And then I got sent to the principal's office, possibly the first kid in my school to get sent there for challenging mathematical principles. <g>

A Different Answer
Several years later, I got a completely different answer:
You want to know what the value of X / 0 is (X being any normal number).
Start by looking at X / A.
You can experimentally determine that whatever number you put on top (X), as you make A smaller and smaller and smaller and smaller, the result gets larger and larger and larger and larger.
You can always make A smaller (by dividing it in half, for example), and so you can always make the result larger.
If there is a limit somewhere as to how small you can make A, then there must also be a limit to how large the result can get.
There *is* a limit to how small A can get: it can get closer and closer and closer to zero, without ever necessarily reaching zero, becuase you always keep making it smaller, but the limit is 0. A can approach zero without ever reaching it, and zero is the limit to how small it can get.
And "infinity" is the limit to how large the result of the division can get. As A gets really tiny, the result gets really big, and approaches "infinity". (That's infinity 1, by the way <g>).
So if it makes you feel better, you can think of the result of dividing any number by zero as being "infinity".
It made me feel better <g>.

Copyright (c) 1998 Richard Grossman, All rights reserved.