On Saturday, March 1, 2014 11:10:43 PM UTC-5, John Gabriel wrote: > On Sunday, 2 March 2014 00:43:02 UTC+2, Dan Christensen wrote: > > > > > You have been unable to derive even the most elementary result from number theory. What kind of "axioms" are they? > > > > Did you perhaps mean that because I am not playing your silly games, that your assertions must be true? :-) > > > > > > Axioms don't need proofs. In fact, they usually can't be proved. > > > > > The statement, for all natural numbers n, n=/=n+1, is not an axiom (in Peano or in your own system). > > > > It is *very much an axiom" by definition of the *natural numbers*. >
Not in the Peano axioms, and not in the supposed "definition" you presented here.
> > > Look you idiot, n = n + 1 for all n => 1 is how the natural numbers are constructed. THERE IS NO NEED FOR PROOF. What an imbecile. >
If you can't prove this most elementary result, what can you prove, John Gabriel? Give us anything at all. Your choice. May I recommend something really, really simple like proving the existence of a number other than 0 using your "axioms" alone. No allusions to "common sense" or "what every 2-year-old knows" -- just YOUR "axioms".