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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Mon, 27 Jan 2025 15:04:21 +0100
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On 27.01.2025 13:49, joes wrote:
> Am Mon, 27 Jan 2025 12:13:38 +0100 schrieb WM:
>> On 26.01.2025 20:06, joes wrote:
>>> Am Sun, 26 Jan 2025 19:08:08 +0100 schrieb WM:
>>
>>>>>> But no actually infinite set is possible.
>>>>>> {1}
>>>>>> {2, 1}
>>>>>> {3, 2, 1}
>>>>>> ...
>>>>>> The length of the first column gives the cardinality.
>>>>> The length? You gave an infinite list. Every column is infinite.
>>>> No row is infinite. No column is longer than all rows. All rows and
>>>> columns belong to potentially infinite collections.
>>> All columns are infinite.
>> No column is greater than all rows. All rows are finite. No column is
>> actually infinite, i.e., has length |ℕ|.
> That’s just wrong. There are OBVIOUSLY infinitely many rows.

Obviously is obviously is not correct.
There are infinitely many rows with infinitely many numbers. 
Nevertheless all rows are of length smaller than |ℕ| and therefore by 
symmetry also the first column is of length smaller than |ℕ|.

Regards, WM