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.

>>5
I don't know much algebra so I'll just tell you what I got from that: a number is an element of any ring which contains Z as a subset (and whose rules for addition and multiplication are identical to that of Z for that subset?). I have yet to parse "the prime ring of any characteristic zero ring 'is' Z also." Wikipedia is little help.

Also, you seem to be implying that Z, Q, R, and C are not merely sets of numbers but instead those sets and the operations (+, x). Is this the correct way of looking at that?