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Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!
Posted:
Jan 10, 2013 1:11 PM
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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
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