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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Mon, 17 Mar 2025 17:11:03 +0100
Organization: A noiseless patient Spider
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On 17.03.2025 16:50, Jim Burns wrote:
> On 3/17/2025 12:58 AM, WM wrote:
>> On 17.03.2025 05:23, Jim Burns wrote:
>>> On 3/16/2025 6:22 PM, WM wrote:
>>>> On 16.03.2025 20:41, Jim Burns wrote:
>>>>> On 3/16/2025 3:27 PM, WM wrote:
> 
>>>>>> The question here is
>>>>>> the index of the first disappearance of Bob.
>>>>>
>>>>> The answer requires you to know what 'finite' means.
>>>>
>>>> Answer using your definition of
>>>> finite index or finite natural number.
>>>
>>> You misunderstand.
>>> I don't need to find out what 'finite' means.

You need not find out it but apply it.
> 
>>> Do you (WM) know what 'finite' means?
>>
>> Yes, it means the index is a natural number.
> 
> That's circular.

No, it is correct by definition of finite.

> You won't or can't answer non.circularly.

In mathematics, particularly set theory, a finite set is a set that has 
a finite number of elements. Informally, a finite set is a set which one 
could in principle count and finish counting. (Wikipedia)

That means it has a natural number of elements.
> 
>> Then apply your version of "finite" and
>> answer at which finite index
>> the first loss in lossless exchange happens.
> 
> After all swaps,

Nothing happens anymore.

> No swap exists immediately before all the swaps.
> No visibleᵂᴹ and no darkᵂᴹ.

Therefore: If Bob disappears, it happens at a finite index. Name it or 
confess that you have used a foolish idea.

Regards, WM