Virgil
Posts:
4,483
Registered:
1/6/11
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Re: Matheology � 198
Posted:
Jan 25, 2013 2:46 PM
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In article
<f4b4b403-c0bc-4e97-895c-7a1637c0be1d@u16g2000yqb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 25 Jan., 14:24, William Hughes <wpihug...@gmail.com> wrote:
> > On Jan 25, 10:01 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >
> > > On 25 Jan., 09:24, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Jan 25, 9:02 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > On 25 Jan., 01:27, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > > > Outside of Wolkenmukenheim it is clear that an infinite set can be
> > > > > > the
> > > > > > union
> > > > > > of finite sets.-
> >
> > > > > But in mathematics it is clear that a strictly increasing sequence
> > > > > does not contain its limit. Each one of infinitely many terms fails
> > > > > to
> > > > > reach the limit. And this case is given by the sequence of finite
> > > > > initial segments of natural numbers.
> >
> > > > From which it follows that the collection of all natural numbers
> > > > (which contains only finite natural numbers)
> > > > is not a finite initial segment of natural numbers.
> >
> > > > So N is not a FISON.
> >
> > > N, if actually existing,
>
> (Note this phrase: "if actually existing".)
>
> is the limit, the set of all natural numbers.
> > > Similarly, 1/9 is not an element of the sequence 0.1, 0.11, 0.111, ...
>
> (Note that 1/9 is not actually existing as a decimal fraction.)
That depends on one's definition of decimal fractions. Some definitions
allow a digit for every FISON.
>
> (One month after first Christmas after end of the world!)
>
> > WM notes that N is not a FISON.-
>
> That N which matheologians believe in!
Then it seems that virtually every real mathematician is also a
matheologician as well, since only a few nuts like WM object to having a
set of all naturals.
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