In article <email@example.com>, firstname.lastname@example.org wrote:
> On Wednesday, 26 February 2014 23:40:13 UTC+1, Dan Christensen wrote: > > > > > But not as the defnition of the natural numbers. The natural numbers can > > > only be defined by the natural process of counting or of adding units, > > > i.e., by the foundation of mathematics. > > > > > > > > In a cognitive or historical sense, perhaps. > > > In the correct sense.
WHich sense is far beyond WM's capability either to produce or understand.
Any set satisfying the Peano postulates can serve as "the" set of natural numbers.
There are already two differing models in common use, one in which 0 is taken the initial natural and another in which 1 is the initial natural, with the former gaining usage, particularly with the growth of computer use, and the latter losing it. --