Re: The set of necessary FISONs

On 1/30/2025 5:36 PM, WM wrote:

On 30.01.2025 19:44, Jim Burns wrote:

On 1/29/2025 3:26 AM, WM wrote:

ω-1, if ω-1 existed,
would need to be both growable¹ and shrinkable¹.

>
It is both.
>

However,
in that case,
ω would need to be both growable¹ and shrinkable¹,

>
It is both.
>

ω+1 would need to be both growable¹ and shrinkable¹,

>
It is both.

It can't both be true that
that ω+1 is both growable¹ and shrinkable¹
and
that ω is the least upper bound of
ordinals both growable¹ and shrinkable¹.
----
For the rooms I refer to,
each room has
an ordinal both growable¹ and shrinkable¹.
and
each ordinal both growable¹ and shrinkable¹
has a room.
For the swaps I refer to,
each pair of
fuller¹(emptier¹), grown¹(shrunk¹) ordinals
has a swap between their rooms,
and
only pairs of
fuller¹(emptier¹), grown¹(shrunk¹) ordinals
have a swap between their respective rooms.
For these rooms and these swaps,
there are no swaps into a room,
except for rooms with a later swap.out.
If, after all swaps,
Bob is still in a room with swap.in,
why didn't its later swap.out swap him out?
If, after all swaps,
Bob is in a room without a swap.in,
how did he get there?
If, after all swaps,
Bob isn't in a room with a swap.in
and isn't in a room without a swap.in,
but Bob is somewhere,
what does it mean for Bob to be somewhere?