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Topic: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR:
THE REALS ARE UNCOUNTABLE!

Replies: 47   Last Post: Jan 12, 2013 11:33 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!

Posted: Jan 10, 2013 1:08 PM

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