Re: The set of necessary FISONs

Am Wed, 19 Feb 2025 17:57:47 +0100 schrieb WM:

Am 19.02.2025 um 13:17 schrieb Richard Damon:
 

Name a FISON that can not be put into a set that is sufficient set, one
whose union is the set of Natural Numbers.

Every FISON. There is no sufficient set. If it is assumed, then F(1) can
be omitted without changing the union of the remainder. And if F(n) can
be omitted without changing this union, then also F(n+1) can be omitted
without changing this union. That makes the omitted FISONs the inductive
collection of all FISONs and proves the implication: If UF = ℕ, then { }
= ℕ.

Dude, you cannot still have the same nonempty union after removing every
element, even if you do not think it is N. Do you think the union of all
FISONs is empty?

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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.