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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Mon, 27 Jan 2025 17:30:44 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sun, 26 Jan 2025 15:28:14 +0100 schrieb WM:
> On 26.01.2025 13:38, Richard Damon wrote:
>> On 1/26/25 3:51 AM, WM wrote:
>>> On 25.01.2025 15:16, Richard Damon wrote:
>>>
>>>> Sure it does, you just need to take the union of an infinite number
>>>> of them.
>>>
>>> But that is impossible because there are not two consecutive actually
>>> infinite sets in ℕ. Since every FISON is followed by an actually
>>> infinite set, ∀n ∈ U(F(n)): |ℕ \ {1, 2, 3, ..., n}| = ℵo, there is no
>>> actually infinite set of FISONs.
Quantifier shift: yes, every FISON, but the successor of the SET of all
FISONs isn’t even defined.

>>>>> FISONs enumerate themselves. There is no infinite FISON and hence no
>>>>> infinite number of them.
>>>> Then, what is the highest FISON?
>>> That depends on the system. All we know is that it is finite.
>> No, it doesn't exist.
> {1}
> {2, 1}
> {3, 2, 1}
> ...
> The first column never gets larger than a FISON.
Neither does it stop.

-- 
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.