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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 11, 2013 1:57 AM
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On 10 Jan., 23:04, Virgil <vir...@ligriv.com> wrote:

> What he, and I, find incomprehensible is why
>    "the anti-diagonal can at no finite position
>     deviate from every entry of the list"
> is presumed to imply
>    "That means it can never deviate from every entry."

At no finite position means never because there are no infinite
positions, in mathematics.
>
> What prevents the diagonal from differing from entry n at position n,
> and thus differing from each entry?

Position n is a finite position. But it is clear that for every finite
position there is a double of the diagonal.
>
> That is the way Cantor described it, and nothing WM has said shows why
> Cantor was not correct.

The first halt sentence is correct.
The second shows your lack of insight: Not at a finite plave means
"never". It does not mean "in some infinity" although matheologians
believe in finished infinity.

Regards, WM

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