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

In article 
<a8ae723e-8a3c-474a-97d3-5bf5b9d56efc@f8g2000yqa.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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 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
countability.

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!
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