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

Am Sun, 12 Jan 2025 12:48:50 +0100 schrieb WM:

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.

Must be unexplainable...

In actual infinity all numbers are present. No one is missing, according
to Cantor. None can be added.

Why should you.

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.

No, not if you really multiply *every* number and not only finitely many.
The *cardinality* is the same.

--
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.