Re: The set of necessary FISONs

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.