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

On 19.01.2025 16:05, joes wrote:

Am Sun, 19 Jan 2025 11:52:33 +0100 schrieb WM:

Cantor claims this also for infinite sets: "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)]

That's not what that means. Some infinite sets are countable, even though
you don't "finish" them. The quote refers to a bijection.

But there is no bijection bijection without completeness: to contain the positive rational numbers completely.

 

There is no step from finite to infinite.

Not in the visible domain. But there is no loss in lossless exchange -
even in the dark domain. There lies your fault.

There is only a limit, which does have different properties.

A bijection concerns pairing of all elements, no limit. And in particular no loss in explicitly lossless exchange.
Regards, WM