Date: Jan 12, 2013 3:56 AM
Subject: Matheology § 191

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...

1, 2
3, 4, 5, 6
7, ...

This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths.

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