Date: Dec 15, 2012 6:03 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: On the infinite binary Tree
On 14 Dez., 22:13, Virgil <vir...@ligriv.com> wrote:

> Note that the very definition of countability requires that a set can be

> declared countable ONLY if one can demonstrate the existence of a

> surjection from the set of naturals to that set.

If that were correct, there was probably no contradiction. At least it

was not as easy to see. But it is not correct. We have another measure

for countability, namely: every subset of a countable set is

countable.

Matheologians like to cheat their audience by the proof that a list of

all meaningful definitions cannot be given. "Meaningful definition"

can not even be defined. But who cares? The set of all finite words is

countable. The set of all meaningful definitions is a proper subset.

Hence it is countable too.

Regards, WM