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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Fri, 10 Jan 2025 18:12:15 +0100
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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:
>>
>>>>> Hint: The set of all natural numbers, IN, does not change.
>>>> So all natural numbers are fixed. Then for every point on the ordinal
>>>> line it is determined whether there is a natural number. Although we
>>>> cannot determine it because most are dark.
>>> There are no points without numbers.
>> As I said. You can prove it when doubling all elements of the set

{1, 2,3, ..., ω}.  (*)

>> 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?

Regards, WM