Date: Mar 30, 2013 6:45 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 30 Mrz., 19:15, Virgil <vir...@ligriv.com> wrote:
> In article
> <ab85409a-eabf-4b68-b505-d194ed33a...@c15g2000vbl.googlegroups.com>,
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 30 Mrz., 10:17, William Hughes <wpihug...@gmail.com> wrote:
> > > On 24 Mrz., 18:09, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > <snip>

>
> > > > > The only difference is that in the second case you consider
> > > > > some subsets of the nodes to be paths, that are not considered
> > > > > to be paths in the first case.

>
> > > > Well, that is a correct description. It implies that these additional
> > > > subsets cannot be distinguished by nodes from the finite subsets

>
> > > Piffle.  It is trivial to distinguish a subset that has a node
> > > at a last level from a subset that does not have a node
> > > at a last level.

>
> > No, that is impossible if an infinite path consists of infinitely many
> > finite subsets.

>
> All infinities consist of infinitely many finite parts.
> But the infinite set of all naturals is distinguishable be from the
> infinite set of all FISONs,


And so is the path of 1/pi distinguishable from all its finite initial
segments which are in the tree. But as you said, 1/pi is not distinct
from them. It comes into tze construction automatically. The limit is
in any case a member of the sequence. That is unmathematical.
>
> > It is impossible to distinguish the actually infinite path of 1/pi
> > from a path that only is built of all finite initial segments of the
> > path of 1/pi.

>
> It may be so in Wolkenmuekenheim, but a set of only finite
> approximations to an irrational number can elsewhere be distinguished
> from the number itself.


Then explain why this is not possible in the Binary Tree. You said
that the irrationals come into the tree automatically, impossible to
distinguish by nodes.

Regards, WM