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Topic: TRANSFINITE would be very weak if there was an alternate theory
Replies: 284   Last Post: Jan 4, 2012 12:18 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: TRANSFINITE would be very weak if there was an alternate theory
Posted: Dec 7, 2011 10:40 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 7 Dez., 21:24, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > > In any sane theory, given any two fisons, one must be a subset of the
> > > > other,

> >
> > > Correct!
> >
> > > And therefore it is not possible that these natural numbers which do
> > > not fit into one FISON could find an asylum in infinitely many other
> > > FISONs.

> >
> > Non sequitur.
> > 2 does not fit into {1} but fits into infinitely many other fisons.
> > 3 does not fit into {1.2}, but fits into infinitely many other fisons.
> > ...
> > n+1 does not fit into {1,2,3,...,n},but fits into infinitely many other
> > fisons.
> > and so on as infinitum.

>
> Your couting does not help.
> All natural numbers that fit into the FISONs, fit into a finite set.

Any such finite set of naturals, like every finite set of naturals,
being naturally ordered, must have a maximum member, whose successor is
a natural not fitting into that set or any of those fisons.
--

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