Date: Jan 14, 2013 6:59 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 191

On 13 Jan., 21:41, Virgil <vir...@ligriv.com> wrote:
> In article
> <4e0deecc-72b6-4e2b-be52-9991cec0e...@10g2000yqk.googlegroups.com>,
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 12 Jan., 23:03, Virgil <vir...@ligriv.com> wrote:
>
> > > > You are invited to "discern" another path from the countable bunch of
> > > > infinite paths that I used to construct the Binary Tree.

>
> > > Until you list the ones that you used, there is no way to "discern"
> > > another, but any list you provide also provides a nonmember.


Here are all paths that I used:

0.
0 1
01 01
...

and so on. Every node that you arrive at allows to continue left or
right. And all that is countable.

> Why should I like to have something which does not exist?

You like it so much, because otherwise you would never have started to
believe in uncountability.
>
> If WM wants to claim such a list exists, then HE is reqponsible for
> proving it, and the only valid proof is to present us with it, or at
> lest some unambiguous rule for generating it.


Follow any desired infinite path of the Binary Tree above, which has
been constructed from all finite initial segments of all paths. You
will never gather more than countably many infinite paths. And you
will never miss any path representing a real number of the unit
interval.

Regards, WM