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Re: Cantor Confusion

Subject: Re: Cantor Confusion
From: Virgil
Date: Sat, 30 Sep 2006 12:23:38 -0600
Newsgroups: sci.math
In article <1159611187.639749.195260@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
 mueckenh@xxxxxxxxxxxxxxxxx wrote:


> Unfortunately, his method fails in some cases which is fatal for an
> impossibility proof. The list, for instance,
> 
> 0.0
> 0.1
> 0.11
> 0.111
> ...
> 
> with the prescription that the diagonal digit 0 is replaced by 1,
> delivers a number which is not different from any list number, except
> in the last digit, which, however, does not exist.

Except that that list is really the list
0.000...
0.1000...
0.11000...
0.111000...
which is the same as the the rational list
0
1/2
3/4
7/8
...
or the base 4 list
0.000...
0.1000...
0.3000...
0.31000...
0.33000...
...
And in this last form, it is easy to construct a number to in the list:
0.222..., for example

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