David,
Are you familiar with Peano's axioms? They describe the natural numbers. I took a
course in the foundation of mathematics in college and was surprised that arithmetic
could be axiomitized just like geometry. And yes, just as you can have different
geometries, you can also have different arithmetics, just as you say.
Check out:
http://mathworld.wolfram.com/PeanosAxioms.html
> What are the axioms of arithmetic? I have said this before, but I would
> really like to discuss it more thoroughly.
>
Glenn
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