Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 18.12.2024 21:15, joes wrote:

Am Wed, 18 Dec 2024 20:06:19 +0100 schrieb WM:

On 18.12.2024 13:29, Richard Damon wrote:

On 12/17/24 4:57 PM, WM wrote:

>

You claimed that he uses more than I do, namely all natural numbers.

Right, you never use ALL the natural numbers, only a finite subset of
them.

Please give the quote from which you obtain a difference between "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)] and my "the infinite sequence f(n) = [1, n] contains all
natural numbers n completely, and each of them only once at a
determined place."

You deny the limit.
 

When dealing with Cantor's mappings between infinite sets, it is argued
usually that these mappings require a "limit" to be completed or that
they cannot be completed. Such arguing has to be rejected flatly. For
this reason some of Cantor's statements are quoted below.