On Thursday, 27 February 2014 20:13:28 UTC+2, Martin Shobe wrote: > On 2/27/2014 11:41 AM, Dan Christensen wrote: > > > On Thursday, February 27, 2014 11:56:50 AM UTC-5, John Gabriel wrote: > > > > > >> > > >> Observe that all the basic arithmetic operations are defined in terms of difference, which is the most primitive operator > > > > > > That's all very nice, but I prefer Peano's five, relatively succinct axioms as a starting point. You can probably derive some equivalent of all your "axioms" from them. And they have the pleasing property of describing the structure at least one subset of EVERY infinite set. > > > > Not really. 2 + 3 = 6 fits the statements he's given. I seriously doubt > > you'd get that from Peano. > > > > Martin Shobe
There is not a chance you would get 2+3=6 from my axioms.