Date: Feb 13, 2013 4:20 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<47d84a88-950f-4091-8dcb-13cdaa3b2e62@z4g2000vbz.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.


No on implied there were. But if not all, name an exception!
> >
> >
> >

> > > > 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?


The n's for which the nth line of the list is not a FIS of d depends on
the list and the d, so

Show me your list and I will show you a 'd' such that

NO line of the list is a FIS of 'd'.
> >
> > 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.


But not any l longer than d, or even as long, if each l is finite.

The point is that for any listing of binary sequences, finite or
infinite, one can define a diagonal which is not listed.

And no matter how loudly WM screams that it is not so, it remains so.
--