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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Thu, 20 Mar 2025 10:10:14 +0100
Organization: A noiseless patient Spider
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On 19.03.2025 23:51, Jim Burns wrote:
> On 3/19/2025 3:19 PM, WM wrote:
>> On 19.03.2025 16:18, Jim Burns wrote:
>>> On 3/18/2025 12:58 PM, WM wrote:
>>>> On 18.03.2025 17:34, Jim Burns wrote:
> 
>>>>> After all the swaps,
>>>>> without ever disappearing into
>>>>> anywhere other than a finite set,
>>>>> Bob disappears out of all finite sets.
>>>>
>>>> No, that is impossible.
>>>
>>> Then there are subsets larger than their sets.
>>
>> No, there are dark numbers. That is enough.
> 
> ⎛ A set is WM.sized ==
> ⎜ membership.change.by.one changes size.
> ⎜ #A < #Aᣕᵃ

If Bob leaves the matrix, then logic is violated. Therefore Bob cannot 
leave the matrix in reasonable mathematics. All your waffle cannot 
change this fact.

Regards, WM