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

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

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.