Numbers

So, um, is there some grand unified theory of numbers? What makes an integer, a fraction, a real, and a complex number all the same thing? What makes, say, a graph, not one of these things?

Also could you tell me how these definitions get decided, because I've been working with a hypothetical King of Math in my head and it just doesn't feel right. He's kind of a jerk.

>>1
1) Z, Q, R, and C are all defined in terms of the natural numbers, but the prime ring of any characteristic zero ring "is" Z also.

And there isn't a ring structure on the set of graphs. (that I know of)  Even if there was, it might not be compatible with the ring structure on any of those other rings. (i.e. you couldn't embed the set of graphs as a subset of C to identify a graph as a number)

I've been working with a hypothetical King of Math in my head

Please report to the nearest free clinic for your prescription for antipsychotics.  Mention this post and recieve your second month free!