Virgil
Posts:
6,967
Registered:
1/6/11
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Re: Matheology � 258
Posted:
Apr 29, 2013 11:14 PM
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In article
<bb7b639b-72de-48b0-81a5-91dcb9787c02@s4g2000vbr.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> It is not possible to list irrationals by writing their decimals.
> Therefore it is not possible to create irrational diagonals of Cantor-
> lists by writing their decimals.
If WM claims that a list of the reals in [0,1] is impossible, he is
conceding the uncountability of that set.
There are two mutually exclusive possibilities:
(1) either there is a COMPLETE list of all real numbers in [0,1],
existence of such a listing being necessary show in order to establish
that the set of reals is countable, or
(2) there is no such listing, and that set of reals, [0,1], is not
countable.
Cantor showed that each and every list of real numbers in [0,1] is
necessarily INcomplete.
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