Date: Dec 15, 2012 7:30 PM
Author: Virgil
Subject: Re: On the infinite binary Tree

In article 
WM <> wrote:

> On 14 Dez., 22:13, Virgil <> 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 or an injection

from that set to the set of naturals.

> 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.

It may be a "measure", whatever that means, and validly establish
countability of subsets of a countable set, or uncountability of
supersets of an uncountable set, but it is not the definition of

And showing that a set is a subset of a set that has been shown to be
countable shows indirectly that the required surjection or injection
must exist.

So that WM loses again!