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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 16 Feb 2025 07:27:34 -0500
Organization: Peripheral Visions
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joes was thinking very hard :
> Am Sun, 16 Feb 2025 11:36:32 +0100 schrieb WM:
>> Am Sat, 15 Feb 2025 17:42:51 +0000 schrieb joes:
>>> Am Sat, 15 Feb 2025 13:56:17 +0100 schrieb WM:
>>>> On 14.02.2025 20:48, Jim Burns wrote:
>>>>> On 2/14/2025 8:02 AM, WM wrote:
>>> 
>>>>>>> The set of rows and the set of columns are both the size of ⋃{F} 
>>>>>>> and each other.
>>>>>> Yes, that is potentially infinite.
>>>>> The set of rows, the set of columns, and ⋃{F} do not change.
>>>> Then it would need to contain ℕ, as an infinite FISON.
>>> Nah. Then it would be finite.
> No further rows would be needed. Actually, the first column is N.
>
>>>>> Bob is not anywhere he has swapped to.
>>>> Then your logic allows lossless exchanges with losses. Not acceptable.
>>> Only in the limit of the permutations, which may not be a permutation
>>> itself.
>> There is no limit in counting if countable sets are really countable.
> Bravo, you wilfully misunderstood „limit”.

He also apparently misunderstands countable.