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

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Posts: 8,833
Registered: 1/6/11
Re: Infinity: The Story So Far
Posted: Mar 8, 2014 5:30 PM
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In article <>, wrote:

> On Saturday, 8 March 2014 00:07:52 UTC+1, Virgil wrote:

> > > 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.

> And what do you conclude?

That 0 is not a successor but that there are successors which are not 0.
> >
> > Before WM pontificates on what the Peano axioms say he really should
> > figure out what they do say.

> They say that there is the number 0 and many successors which need not be
> numbers.

I am not aware of Peano ever explicitly saying that successors need not
be numbers. The most one can properly claim is that Peano does not
explicitly say they must be numbers.

But such carefulness with the truth is well beyond WM's capabilities.

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