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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 16 Feb 2025 12:11:05 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sun, 16 Feb 2025 11:39:45 +0100 schrieb WM:
> Am Sat, 15 Feb 2025 17:54:05 +0000 schrieb joes:
>> Am Sat, 15 Feb 2025 12:50:40 +0100 schrieb WM:
>>> On 14.02.2025 19:02, Richard Damon wrote:
>>>> On 2/14/25 11:28 AM, WM wrote:
>>> 
>>>>> The definition is that it is a set of FISONs which has a smallest
>>>>> element that is not as useless as a cup of coffee.
>>>> Which, as I said, is a definition in Naive Set theory,
>>> Obviously you have no clue of set theory, be it naive or advanced.
>>> Every set of ordinals has a smallest element. Look up the notion of
>>> well-order.
>> No, that is not the definition. No element of the set of FISONs is
>> necessary
> Therefore all can be removed, and U(F) = ℕ ==> U(F\F) = ℕ.
No, obviously you can’t remove all („which one is necessary?” my ass).
That the union of the empty set is not N has no bearing on the matter.

>> (though one could be, if we wouldn’t agree that none is)
>> for their union to be N. *That* set has a smallest element, as does
>> every other infinite set of FISONs (the nonempty finite sets do as 
>> well, but their union is not N, but the largest FISON). Now you come 
>> along and claim that the empty set should have a first element.
-- 
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.