Date: Feb 13, 2013 9:27 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 13 Feb., 09:48, Virgil <vir...@ligriv.com> wrote:
> In article
> <1b2bb717-425f-488d-b50c-e442f20af...@fe28g2000vbb.googlegroups.com>,
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 12 Feb., 20:40, William Hughes <wpihug...@gmail.com> wrote:
> > > > What do you understand by being equal "as potentially infinite
> > > > sequences"?
>
> > > two potentially infinite sequences x and y are
> > > equal iff every FIS of x is a FIS of y and
> > > every FIS of y is a FIS of x.
>
> > Every means: up to every natural number.
>
> Which includes being up to all natural numbers.

No. After all there is nothing after all natural numbers.
>
>
>
> > > You can use induction to show that two potentially
> > > infinite sequences are equal  (you only need
> > > "every" not "all").
>
> > Up to every n there is a line l identical to d.
>
> Only in Wolkenmuekenheim.

For which n is this line lacking?
>
> Since for every line of length n, d is of length at least n+1, at least
> everywhere else besides Wolkenmuekenheim, WMs claim does not hold true
> outside it.

For every line of lenght n there is a line of length n^n^n, so d of
legth n+1 has no problems with accomodation.
>
> And inside Wolkenmuekenheim all lines are finite.

Do you know of an infinite line? A line inexed by omega, for instance?
>
>
>
> > For every FIS of d there is a line. You cannot find a line for all FIS
> > (because all FIS do not exist).
>
>  But for each finite line l,there is  FIS of d longer than l.

Again for each FIS of d there is a longer l.

Regards, WM