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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 3:56 AM

On 25 Jan., 09:20, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 25, 9:11 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 25 Jan., 09:07, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Jan 25, 8:57 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > >   "Write a sequence like xxxxxxxxxx... and do never stop"
>
> > > Perfectly acceptable finite description of an infinite sequence.
>
> > Of course, nothing however that could be diagonalized in a Cantor-list
> > or could be the result of diagonalization.

>
> Why not?  The diagonalization of a list with finite description is a
> finite
> desciption.

The diagonalization of finite descriptions does not necessarily supply
a description at all.
>
> Consider the list with every element 0
>
> The result of diagonalization is 111...
>
> (from which it follows that there is no finite description of
> all infinite sequences with finite description.)

That is of no interest here. Of interest is this: If the same set of
nodes has to describe both, the Binary Tree with finite paths and that
with infinite paths, then it is impossible to discern, alone by nodes,
whether we work in the former or the latter. Hence I can assert that I
always work in the Binary Tree with finite paths only. I can
diagonalize the complete list of terminating decimals without leaving
the domain of terminating decimals.

Notice, this would only be the case if the domains could not be
distinguisged by nodes or digits, as you mistakenly claimed.

Regards, WM