In article <email@example.com>, firstname.lastname@example.org wrote:
> On Thursday, 27 February 2014 15:26:12 UTC+1, Dan Christensen wrote: > > > > > Repeated succession is, for instance, 1, 2, 4, 8, ... > > > > > > > > > > > > > You are using the word in a different sense here. As should be clear from > > my example, I meant x+1 = S(x), x+2 = S(S(x)), x+3 = S(S(S(x))), ... where > > S is the usual successor function on N. > > You cannot use this N if you require that Peano defines it. Where does he > axiomatize that the difference is always 1?
Wherever does Peano say it cannot be?
As far as I can see in the Peano axioms, S(x) = x+1, even if not required, is allowable. --