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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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 Zaljohar@gmail.com Posts: 2,665 Registered: 6/29/07
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!

Posted: Jan 10, 2013 1:07 PM

On Jan 10, 2:31 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 10 Jan., 12:11, Zuhair <zaljo...@gmail.com> wrote:
>

> > > The anti-diagonal up to digit n must have a double up to digit n.
>
> > Of course, because the list is defined as the list of ALL terminating
> > decimal representations. That is correct and natural and Cantor's
> > arguments Agrees with that completely.

>
> Can you quote the relevant paragraph?
>
>
>

> > > Result: The diagonal cannot be an entry of the list.
>
> > the list
> > ONLY contains TERMINATING decimal representations, while the diagonal
> > and the anti-diagonal are non terminating decimal representations

>
> I do not know what you worship . Every finite initial segment of the
> anti-diagonal is an entry of the list. I do not know what else can
> belong to the anti-diagonal. But certainly this additional thing
> cannot be used to distinguish it from anything.

What I meant is that Cantor, I and everybody who knows basic logic
knows very well that NO such a diagonal (actually no such a real)
could ever exist. And also I meant that any NON terminating decimal
expansion of a real would already be not on the list of yours by
definition even though we know that EVERY n-initial segment of it
would have an n-sized copy of it in the list of course, the reason
because any NON TERMINATING decimal expansion of any of reals is NON
terminating and your list only contains terminating expansions. So
there is a kind of irrelevance here. Anyhow this is not the major
issue. The major issue is that Cantor NEVER claimed that there exist a
diagonal (or anti-diagonal) that has some n-initial segment of it that
is different from every n sized decimal expansion, and you simply
though that he did, so you've misinterpreted Cantor.

Zuhair

>
> > of course the diagonal and the anti-diagonal cannot be
> > different (at a finite position) from all entries of the list, because
> > the list is of ALL finite initial segments of reals, Cantor agrees to
> > that,

>
> Can you quote the paragraph where it does that?
>
> Regards, WM