## Tuesday, 1 March 2011

### Dividing by zero...

It hurts me to type a/0 with the thought that it can be solved, dividing by zero is quite well known to be undefined, but why? Well first of all we need to think about what division is, in a literal sense. It's the inverse operation of multiplication, and thinking about it in this way will help you understand why you can not divide by 0.

10/5=2 and thus when we rearrange this to show division as an inverse of multiplication; 5*2=10. If we think about this with respect to dividing by 0...

10/0=x then; x*0=10 and there is no number that when it is multiplied equals to 10 and thus the answer is undefined. A common misperception is that when you divide by zero it equals to infinity. This assumes that ∞*0=n (where n is any number), which just makes no sense as when you multiply anything by 0 it equals to 0, and 0 does not equal anything. I'd assume that this originated from n/≈0, but it is only roughly equal to 0, not precisely nothing.

Then you may be asking why 0/0 is also undefined. It's for the simple reason that anything multiplied by 0 also equals 0, so the answer could be literally anything and thus it can not be defined.

Zero, is a very strange number and I will do a post on it at a later stage.