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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 27 Oct 2024 14:00:35 -0400
Organization: i2pn2 (i2pn.org)
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On 10/27/24 12:20 PM, WM wrote:
> Am 27.10.2024 um 12:38 schrieb Richard Damon:
>> On 10/27/24 3:38 AM, WM wrote:
>>> Am 26.10.2024 um 21:35 schrieb Chris M. Thomasson:
>>>> On 10/26/2024 9:04 AM, WM wrote:
>>>>> On 26.10.2024 05:21, Jim Burns wrote:
>>>>>> On 10/25/2024 3:15 PM, WM wrote:
>>>>>
>>>>>>> Mainly, among other points, the claim that
>>>>>>> all unit fractions can be defined and the claim that
>>>>>>> a Bob can disappear in lossless exchanges.
>>>>>>
>>>>>> The proof that all unit fractions can be defined
>>>>>> is to define them
>>>>>> as reciprocals of positive countable.to.from.0 numbers.
>>>>>>
>>>>>> That describes all of them and only them.
>>>>>
>>>>> No, you falsely assume that all natnumbers can be defined.
>>>>
>>>> Huh? Confusing to me. Humm... Are you trying to suggest that a 
>>>> natural number can _not_ be a natural number?
>>>
>>> No. But most natnumbers cannot be defined. This can best be 
>>> understood by the unit fractions.
>>
>> So, what is the line between the DEFINED natural numbers and the "not 
>> defined"?
> 
> There is no line. The defined natural numbers are a potentially infinite 
> set, i.e. it can grow without end.
> 
> Regards, WM
> 

So, you agree that there are no undefined Natural Numbers to be dark, as 
the set of that defined Natural Numbers grow without end.

Thus, you also seem to be saying that your "dark numbers" aren't in that 
set of Natural Numbers, and thus don't also make any actual Unit Fractions.