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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: Thu, 23 Jan 2025 09:32:14 +0100
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On 22.01.2025 13:10, Richard Damon wrote:
> On 1/22/25 5:36 AM, WM wrote:
>> On 22.01.2025 00:41, Richard Damon wrote:
>>> On 1/21/25 7:48 AM, WM wrote:
>>>> On 21.01.2025 13:17, Richard Damon wrote:
>>>>
>>>>> the matching happens as a collective whole. It can't complete if 
>>>>> you don't move from the individual step to the collective step.
>>>>
>>>> So it is.
>>>>
>>> And thus,
>>
>> there are visible and dark numbers. As you said: We have to move from 
>> the individual step to the collective step.
>>
> But the numbers being used didn't change, only the logic.

Numbers do not change. Only their state of being known.
> 
> I guess when we talk about the set { 0, 1, 2, 3, ... } you must be 
> defining "4" as a "dark number" as that was the point we shifted from 
> listing them individually to collectively. 

No. Every number that is defined in a system by its FISON is visible. 
Many numbers smaller than 10^99 are defined on the pocket calculator. No 
greater number can be defined in that system.
> 
> The basic problem with your "dark numbers" is that no number itself is 
> "dark", the collective nature is just how we chose to use that number.

It is how we *can* chose them.

Regards, WM