Re: The set of necessary FISONs

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”.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.