Date: Jan 12, 2013 6:45 AM
Author: Zaljohar@gmail.com
Subject: Re: Matheology § 191
On Jan 12, 11:56 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> Matheology § 191

>

> The complete infinite Binary Tree can be constructed by first

> constructing all aleph_0 finite paths and then appending to each path

> all aleph_0 finiteley definable tails from 000... to 111...

>

No it cannot be constructed in that manner, simply because it would no

longer be a BINARY tree.

> 0

> 1, 2

> 3, 4, 5, 6

> 7, ...

>

> This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths.

>

The complete Binary tree contains 2^aleph_0 paths and 2^aleph_0 paths

is strictly greater than aleph_0, this is pretty much standard stuff

that most mathematicians actually all leading mathematicians of the

last century and this one hold to be true.

> If there were further discernible paths, someone should be able to

> discern one of them. But since all possible combinations of nodes

> (including all possible diagonals and anti-diagonals of possible

> Cantor-lists) that can occur in the mathematical discourse already are

> present, a human being cannot discern anything additional.

>

> Matheologians may claim that God can discern more. But God is not

> present in mathematics. Mathematicians have no pipeline to God, as

> Brouwer put it. At least God does never reveal mathematical secrets.

> Or has any reader ever heard God tell a mathematical secret?

>

> Regards, WM