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Topic: Infinity: The Story So Far
Replies: 7   Last Post: Mar 9, 2014 8:52 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Infinity: The Story So Far
Posted: Mar 7, 2014 6:07 PM
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In article <c45329f0-ef48-4e50-96e4-c0b1192c1792@googlegroups.com>,
mueckenh@rz.fh-augsburg.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.
--





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