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Topic: Matheology § 198
Replies: 40   Last Post: Jan 26, 2013 6:54 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 198
Posted: Jan 25, 2013 2:46 PM

In article
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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