In article <email@example.com>, firstname.lastname@example.org wrote:
> My book gives the correct axioms. > > > For over a century now, I think Peano's axioms have been the standard, > > Like Cantor's nonsense. Where do they define that the difference must always > be 1?
They don't. They only requires that each member of a Peano set have a unique successor member, but do not require any specific 'difference' up front. It is only later, after all the basic axioms are satisfied, when defining addition that any "1" appears. --