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

Am Fri, 10 Jan 2025 20:22:44 +0100 schrieb WM:

On 10.01.2025 19:36, joes wrote:

Am Fri, 10 Jan 2025 18:12:15 +0100 schrieb WM:

On 10.01.2025 17:50, joes wrote:

Am Fri, 10 Jan 2025 17:42:39 +0100 schrieb WM:

On 10.01.2025 14:09, joes wrote:

Am Fri, 10 Jan 2025 10:52:46 +0100 schrieb WM:

 

As I said. You can prove it when doubling all elements of the set

{1, 2,3, ..., ω}.  (*)

You mean N u {w}.

Yes.

Your notation misleadingly implies predecessors to omega.

The regular distance of next neighbours remains as a conserved
property in correct mathematics.

Points don't even exist without the numbers. There is no number with
a finite distance from omega.

Since all natural numbers existing below ω are multiplied by 2, when
doubling the elements of (*), no further numbers below ω can be
created - in actual infinity. What happens with the new 50 % of even
numbers?

Why do you want to include omega?

Why not?

It is not a natural number and destroys the symmetry.

What new numbers? There are no evens above omega.

If actual infinity is invariable, then we can take the set ℕ and
consider it as invariable. When we add further elements, it grows.

The set N u {w}, for example, is not equal to N. You can't call
that invariable.

Afterwards it contains further elements. Same can be accomplished by
multiplying all natural numbers by 2.

There is no natural n such that 2*n is not natural.

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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.