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Virgil
Posts:
8,833
Registered:
1/6/11


Re: Infinity: The Story So Far
Posted:
Mar 7, 2014 6:07 PM


In article <c45329f0ef484e5096e4c0b1192c1792@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Friday, 7 March 2014 22:01:11 UTC+1, Virgil wrote: > > > > > > Or require that successors of different members are not themselves > > > > different? > > These successors need not be numbers at all. But they may be, and often are, even if not always naturals. > > > > > > > > Then WM's version of those Peano axioms must then be quite different
> > from any standard English versions which explicite... > > say that every number has a successor, but do not state that there are more > numbers than 0
Actually the Peano axioms do state that. Expicitely! One of them says explicitely that 0 is not a successor.
Before WM pontificates on what the Peano axioms say he really should figure out what they do say. 



