Date: Jan 12, 2013 6:45 AM
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.
> 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