Re: The set of necessary FISONs

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.

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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.