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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 5 Dec 2024 09:46:42 +0100
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On 04.12.2024 19:22, FromTheRafters wrote:

> I like to look at it as {0,1,2,...} has a larger 'scope' of natural 
> numbers than {1,2,3,...} while retaining the same set size. It does this 
> by not being finite.

No, the sets of algebraic numbers and of prime numbers have very 
different sizes. The "bijection" holds only for such elements which have 
almost all elements remaining as successors. The latter cannot be 
paired. They always remain dark.

Contrary to that Cantor believed that all elements are in the bijection: 
"The infinite sequence thus defined has the peculiar property to contain 
the positive rational numbers completely, and each of them only once at 
a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]

Your belief is an incredible mass hysteria because it is so obviously wrong.

Regards, WM