Date: Jan 14, 2013 4:33 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 191

On 14 Jan., 21:53, Virgil <vir...@ligriv.com> wrote:

> > 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.
>
> The number of nodes involved is countable, but every countable set has
> uncountably many subsets,

but most subsets of the set of nodes do not describe paths.
>
> I believe the proofs that no set can be surjected to its power set are
> valid, and will continue to believe it until I see an EXPLICIT
> surjection from some set to its power set.

You could also require an explicit bijection of the set of unicorns to
the naturals - otherwise you are convinced that there are uncountably
many unicorns.

> > You
> > will never gather more than countably many infinite paths.
>
> Then we will never access all of the Complete Infinite Binary Tree, even
> though it does exis.

Where? It seems you yet need God in matheology.

Regards, WM