Re: The set of necessary FISONs

Am Wed, 29 Jan 2025 09:26:35 +0100 schrieb WM:

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.

Or the other way around: there is no room where she can stay,
she will be swapped out of every room.

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

One exception exists: ω-1.

No. If it were finite, it had an initial segment.

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.

Exactly, when it pleases you.

|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.

Aha!

But its union cannot be ℕ because a non-empty
set of FISONs would be necessary.

Why should a necessary set exist?

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.

But not all at once, only every single one. Maybe you can prove that
you can even leave out two at a time?

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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.