Virgil
Posts:
8,833
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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