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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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 Virgil Posts: 8,833 Registered: 1/6/11
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Posted: Jan 10, 2013 4:46 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 10 Jan., 19:11, Zuhair <zaljo...@gmail.com> wrote:
> > On Jan 10, 9:08 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >

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

>
> I would easily get it if you could identify a path that supports your
> assertion by being identified by nodes. Prove your claim by
> identifying a path that is missing

We cannot determine whether a path is missing until we have a list of
the paths which are not missing (and, as WM claims that there are only
countably many paths, such a list is necessarily possible).

> Unless you cannot do that I think that your
> babbling about more than countably many paths

the existence of a countable infinity, which is all that is needed for
Cantor's diagonal argument to prove existence of an uncountable one.
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