Date: Jan 10, 2013 1:11 PM
Author: Zaljohar@gmail.com
Subject: Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF<br> CANTOR: THE REALS ARE UNCOUNTABLE!
On Jan 10, 9:08 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 10 Jan., 18:47, Zuhair <zaljo...@gmail.com> wrote:

>

> > On Jan 10, 1:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > So accordingly we

> > can discriminate a number of reals up to the number of all Omega_sized

> > tuples of finite initial segments of reals,

>

> As omega is not a finite number, you have no finite

> distingusihability.

>

> > and this would be Aleph_0

> > ^ Aleph_0 and we have NO intuitive justification to say that the

> > number of such tuples is countable.

>

> 2^aleph_0 would be sufficient.

>

> That is an argument made by

>

> > INTUITIVE analogies using similes that are fairly natural. Anyhow I do

> > conceded that using such intuitive similes is not that easy to grasp,

> > many people would find it difficult to follow. However the result is

> > that there is NO intuitive grounds to say that the number of all reals

> > are countable.

>

> But there is a striking ground that is more fundamental than any wrong

> or correct logical conclusion, namely that you cannot find out any

> real number of the unit interval the path-representation of which is

> missing in my Binary Tree constructed from countable many paths. At

> least by nodes, you cannot distinguish further reals, can you?

>

> Regards, WM

Your binary tree have UNCOUNTABLY many paths each defined as a

sequence of labels of its NODES, even though it has countably many

nodes. That's what you are not getting. Anyhow.

Zuhair