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

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

On 18.01.2025 19:38, Jim Burns wrote:

On 1/18/2025 3:41 AM, WM wrote:

On 18.01.2025 00:08, Jim Burns wrote:

 

The finite extends much further than you (WM) think it does.
Infinitely further than you think it does.

No.
As long as you deny Bob's existence and violate logic you are not a
reliable source.

 
https://en.wikipedia.org/wiki/Finite_set ⎛
⎜ Informally, a finite set is a set which ⎜ one could in principle
count and finish counting.

 
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.

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.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.