Date: Feb 18, 2013 9:19 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<c6dfe3b2-29d3-4d26-86ad-59f8db09b318@ia3g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 17 Feb., 22:43, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <2199d024-064f-4369-b38d-f1d1cdf2c...@d11g2000yqe.googlegroups.com>,
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > On 17 Feb., 20:05, William Hughes <wpihug...@gmail.com> wrote:
> > > > On Feb 17, 6:49 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > ards, WM

> >
> > > > Ok we have WM statement 1.
> >
> > > >    There is a line l such that
> > > >    l and d are coFIS.

> >
> > > There is no d!
> > > There is for every FIS of d a FIS of a line.

> >
> > If there were no d, then WM would not keep talkimg as if there were one.

>
> There is no actually infinite d.


And there is no finite diagonal, d, at least anywhere outside
Wolkenmuekenheim, for a list of lines whose nth line is of length n and
for which there is no last line.

And outside of Wolkenmuekenheim "INfinite" merely means not finite.

And outside of Wolkenmuekenheim one satisfactory definition of
finiteness of a set is that a finite set does not allow any injection
from itself to any of its proper subsets.

And outside Wolkenmuekenheim, one cannot speak of sets whose membership
is ambiguous. so that the oxymoron "potentially infinite set" is
nonsense. Sets are actual or nonsensical.

So a set which is not finite is either infinite or not a set.
And a list which is not finite is either infinite or not a list.

Thus WM is claiming no d at all. whereas outside Wolkenmuekenheim,
non-finite d's for non-finite lists of ever increasingly long lines is
de rigueur.
>
> > > On the contrary! For every natural number the n-th line and d_1, ...,
> > > d_n are coFIS.

> >
> > Not in this world!

>
> 123...n and 123...n have the same FISs.


But
123...n
and
1,12,123,...,123...n
do not.

LINES of list L:

l_1 = (x1)
l_2 = (x1,x2)
l_3 = (x1, x2, x3)
etc.

FISs of list L:

FIS_1(L) = (l1) = ((x1))
FIS_2(L) = (l1, l2) = ((x1),(x1, x2))
FIS_3(L) - (l1, l2, l3) = ((x1), (x1, x2), (x1, x2, x3))
etc.

Whereas the diagonal is given by d = (x1, x2, x3, ...) so

FISs of diagonal d

FIS_1(d) = (x1) = l_1
FIS_2(d) = (x1, x2) = l_2
FIS_3(d) = (x1, x2 x3) = l_3

so that there is no n for which FIS_n(L) = FIS_n(d).

And with an antidiagonal, things are even worse for WM.
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