Date: Feb 10, 2013 7:30 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <hoqdnWmpiaOtvYXMnZ2dnUVZ_s2dnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> On 2/10/2013 4:16 PM, Virgil wrote:
> > In article
> > <3a8b891b-172f-415f-b4f6-34f988abae5d@e10g2000vbv.googlegroups.com>,
> > WM <mueckenh@rz.fh-augsburg.de> wrote:
> >

> >> On 10 Feb., 18:40, William Hughes <wpihug...@gmail.com> wrote:
> >>> On Feb 10, 10:51 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >>>
> >>>
> >>>
> >>>
> >>>

> >>>> On 9 Feb., 17:36, William Hughes <wpihug...@gmail.com> wrote:
> >>>
> >>>>>>> the arguments are yours
> >>>>>>> and the statements are yours-

> >>>
> >>>>>> Of course. But the wrong interpretation is yours.
> >>>
> >>>>> How does one interpret
> >>>>> we have shown m does not exist
> >>>>> (your statement)

> >>>
> >>>>> to mean that
> >>>
> >>>>> m might still exist
> >>>
> >>>>> ?
> >>>
> >>>> TND is invalid in the infinite.
> >>>
> >>>> Regards, WM
> >>>
> >>> In Wolkenmeukenheim, we can have
> >>> for a potentially infinite set
> >>>
> >>> we know that x does not exist
> >>> we don't know that x does not exist
> >>>
> >>> true at the same time.

> >>
> >> Is it so hard to conclude from facts without believing in matheology?
> >>
> >> The diagonal of the list
> >> 1
> >> 11
> >> 111
> >> ...
> >>
> >> is provably not in a particular line.
> >> But the diagonal is in the list, since it is defined in the list only.
> >> Nothing of the diagonal can be proven to surpass the lines and rows of
> >> the list.

> >
> > It is not that the diagonal "surpasses" any particular line, it is
> > merely that an appropriately defined "diagonal" is different from each
> > and every particular line, i.e., does not appear as any line among the
> > lines being listed.

>
> Yes. And the scare quotes are nice.
>
> The problem with singular terms means that
> "diagonal" is, in fact, a plurality of acts
> of definition.


The Cantor antidiagonal rule, for an actually infinite list of actually
infinite binary sequences is a quite finite rule :

If the two possible values are 'm' and 'w', then the nth term of the
diagonal is to be not equal to the nth term of the nth listed sequence,
meaning that
if the nth term of the nth listed sequence is "m"
then the nth listed element of the diagonal is "w"
and
if the nth term of the nth listed sequence is "w"
then the nth listed element of the diagonal is "m".

In this way, the constructed sequence differs from the nth listed
sequences at lest at its nth postion
--