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

On 12.01.2025 12:59, FromTheRafters wrote:

WM submitted this idea :

On 11.01.2025 15:09, FromTheRafters wrote:

joes laid this down on his screen :

Am Sat, 11 Jan 2025 11:04:56 +0100 schrieb WM:

>

If Cantor has constructed a sequence containing all even numbers of the
original set ℕ, then the doubled even numbers are missing.

What? Doubled even numbers are also even numbers.

>
He's a hopeless case.

>
Yes, you cannot hope ever to understand the difference between potential and actual infinity.

 I've yet to see any useful application of the notion of potential infinity.

All classical mathematics uses it. "In analysis we have to deal only with the infinitely small and the infinitely large as a limit-notion, as something becoming, emerging, produced, i.e., as we put it, with the potential infinite." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (1925) p. 167]

IMO it was created to appease the philosophers and later rejected as useless by modern mathematicians.

They use it too. Otherwise doubling of all natural numbers generates new numbers. But they are too stupid to understand that.

 

In actual infinity all numbers are present. No one is missing, according to Cantor. None can be added.
If you multiply every number by 2, then larger even numbers than all hitherto present even numbers are created because the number of numbers remains constant but the odd numbers disappear.

 Wrong, the numbers are not 'created' as they already existed.

All existing numbers have been doubled. That creates a new set.
Regards, WM