Re: Cantor's diagonal proof wrong?
From: Rasmus Villemoes (burner+usenet_at_imf.au.dk)
Date: 11/14/04
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Date: Sun, 14 Nov 2004 18:14:39 +0100
curt@kcwc.com (Curt Welch) writes:
> So, let me create a mapping. I'll start with the mapping from the integers
> to the reals in the range 0 to 0.99999....
>
> I R
>
> 0 0.0000...
> 1 0.1000...
> 2 0.2000...
>
> 10 0.0100...
>
> 123 0.3210...
>
> So you just reverse the digits in the integer to create the real. I claim
> this mapping is one to one and covers all the reals in that range.
The same (or at least nearly the same) mapping was used in an arXiv
article some time ago. A few weeks later, the author posted another
article with a corollary to the above 'theorem' (that the mapping
is bijective). The corollary stated "Not every integer is finite".
-- Rasmus Villemoes <http://home.imf.au.dk/burner/>
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