Re: The set of necessary FISONs

Am Thu, 30 Jan 2025 23:32:52 +0100 schrieb WM:

On 30.01.2025 15:30, Richard Damon wrote:

On 1/30/25 4:14 AM, WM wrote:

On 29.01.2025 13:46, Richard Damon wrote:
>

We can in fact build an infinite set of infinite sets of FISONs whose
union is the set of Natural Numbers,

>

If there is a set with U(F(n)) = ℕ, then it has a first element that is
not completely useless.

Not necessarily. You may add the smallest segment that is not in the
set to be unified (if the set does not include all). A sufficient
set does not imply a necessary subset; indeed, a necessary set may
not exist at all. It would require that a number existed in only one
segment; however every segment is a subset of the successors.

But all F(n) can be shown to be completely
useless because infinitely many natnumbers are missing.

Again: every single one, or even an arbitrary finite number.
If you have inf. many segments, you obviously have inf. many
numbers.

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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.