On Tuesday, March 4, 2014 1:47:02 PM UTC-5, John Gabriel wrote: > Dan Christensen wrote: > > > > > I am glad that we can finally agree that these are indeed these 5 essential properties of the natural numbers (from Peano's axiom). And that from them, all their other properties can derived. > > Well, the first "axiom" is not a property. >
It is an essential property of the natural numbers: there exists at least one element of N. N is not an empty set. As you are now aware, if you don't admit such a property, your "axioms" will get nowhere. You need some kind of starting point. You won't be able to prove the existence of even a single natural number otherwise. How embarrassing for you. But you are over that now, right, John Gabriel?