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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 6:31 AM

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.

> 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