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

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 198
Posted: Jan 25, 2013 4:01 AM

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, 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, ...

The limit 1/9 differs from all terms of the sequence, not only from
every term.
The limit N differs from all FISONs, not only from every FISON.

Regards, WM