On Wednesday, March 5, 2014 1:07:36 PM UTC-5, John Gabriel wrote:
> > So tell me, what is a number in one sentence? :-) Don't write an essay. Just tel...
A number is an element of the set N as defined by Peano's axioms as above.
But this is just an informal comment. Construct your own more convoluted sentence if you don't like it. It doesn't really matter.
To begin formally deriving number theory, however, we just list Peano's axioms at the beginning of each proof an proceed, using the rules and axioms of logic and set theory. You don't seem to grasp that essential point, John Gabriel. You don't think beyond your definition to how you are going to apply it. If you actually tried you use your definition to, say, prove the associativity of addition, I think you would soon see several gaping holes in your informal narrative.