Re: The set of necessary FISONs

On 28.01.2025 17:29, Jim Burns wrote:

On 1/28/2025 10:29 AM, WM wrote:

On 28.01.2025 14:10, Jim Burns wrote:

 

A set such that a larger FISON does NOT exist
is sufficiently large in order for Bob
to disappear purely from swaps within the set.

>
He disappears from visibility.

 There are no swaps into a room,
except for rooms with a later swap.out.

No.

 Darkᵂᴹ or visibleᵂᴹ,
there are no swaps into a room,
except for rooms with a later swap.out.

One exception exists: ω-1.

I use Cantors actual infinity:

 Only when it pleases you to do so.

No I use it in order to show its consequences. In my personal opinion potential infinity appears preferable.

 

|ℕ| is a fixed quantity
larger than all natural numbers.
What is your infinity?

The union of all FISONs is infinite.

Yes, it has no last FISON. But its union cannot be ℕ because a non-empty set of FISONs would be necessary. But the set has no elements, because for every FISON of the assumed set we can prove that it is useless and could be dropped.

What are you (WM) most recently calling it?

It is a potentially infinite collection.
Regards, WM