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