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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 4:49 PM

On 11 Jan., 01:35, Virgil <vir...@ligriv.com> wrote:

Do you think that the union of the set of finite initial segments of
paths
0.1
0.11
0.111
...
contains the path 0.111...
or not?
If not, what node is missing? None.
So how would you distinguish by nodes the path 0.111... from the union
of its finite initial segments?
If yes, how could the infinite path 0.111... be distinct from the
union of its finite initial segments?

Regards, WM