Ok that made it more clear guys, thanks. Kinda turns me off how so much of mathematics depends on categorizations with unintuitive names (e.g. odd/even) and unintuitive definitions. But I do think it is interesting to define properties of numbers, and kinds of numbers, which I guess is what mathematics tends to do.

odd / even is pretty intuitive as far as math names go. I think of it like if you're dividing things into pairs, for an odd number of things there will be an odd one left, whereas for an even number of things it will all even out.

Now look at names like "derivative", "integral", "radical", "modulus" etc and I understand. For abstract concepts like you see in a lot of math it is hard to come up with an intuitive name.

Now someone answer the rephrased question Mixa mistook mine for

I think SK's link dove into this topic a bit. Or

http://en.wikipedia.org/wiki/Zero. Anyway, here's my attempt at an explanation:

Basically the number zero was invented because it makes it easier to think about math when you have zero. It's possible to do math where you only have 1 2 3 4 etc but then you get stuck with questions like what is 4-4? And this is a question that can come up pretty easily in real life (if I have 4 apples and you steal 4 of them then how many apples do I have?) so coming up with a number called 0 allows me to think more easily about these questions.

It's really the same reason that we invented negative numbers, rational numbers, real numbers, and complex numbers. It's just that the need for the number 0 is a lot more obvious than the need for i or 7/3 or -57