On Thursday, February 27, 2014 10:35:11 PM UTC-5, John Gabriel wrote: > On Friday, 28 February 2014 01:43:52 UTC+2, Dan Christensen wrote: > > > > > As I asked WM, can you prove that n=/=n+1 in your system? > > > > It's unnecessary to prove n=/=n+1 because n < n+1 by definition since n is a natural number.
So, this is another axiom?
How about the associativity of + and *? Two more axioms? How about their commutativity? Yet two more axioms? How about their cancelability, etc., etc.....
I think you will need some equivalent of the Peano's 5th and most important axiom: the principle of induction. You really can't do number theory without it.