On Friday, February 28, 2014 2:21:51 PM UTC-5, iwa...@gmail.com wrote: > On Friday, February 28, 2014 9:08:25 PM UTC+2, fom wrote: > > > > > I should have said definition. > > > > > Book 7, Definition 1 > > > A unit is that by virtue of which each of > > > the things that exist is called one. > > > > I am not going to enter a discussion about Euclid with you because you don't know anything about Euclid. I never ignored that first definition. In fact, I defined a unit in my axioms - far better than Euclid. >
Looks like you had better add all the axioms of Euclidean geometry to your list of "axioms" (preferably from Tarski). Maybe another 10 or 20 axioms/definitions (many counter-intuitive as I recall)? Maybe you should consider NON-Euclidean as well -- one less axiom. But you still won't be unable to do proof by induction.
Are you ready to give Peano a chance now, John Gabriel? Just 5 simple little axioms. 4 of them devoted to describing nothing more than an injective, but non-surjective function on a set. The other is a simple statement of... wait for it... THE INDUCTION PRINCIPLE. And you will have all of number theory at your disposal.
Leave the Dark Side once and for all, John Gabriel. Trolldom really isn't for you.