Re: The non-existence of "dark numbers"

On 3/20/2025 5:10 AM, WM wrote:

On 19.03.2025 23:51, Jim Burns wrote:

On 3/19/2025 3:19 PM, WM wrote:

On 19.03.2025 16:18, Jim Burns wrote:

On 3/18/2025 12:58 PM, WM wrote:

On 18.03.2025 17:34, Jim Burns wrote:

After all the swaps,
without ever disappearing into
anywhere other than a finite set,
Bob disappears out of all finite sets.

>
No, that is impossible.

>
Then there are subsets larger than their sets.

>
No, there are dark numbers. That is enough.

>
⎛ A set is WM.sized ==
⎜ membership.change.by.one changes size.
⎜ #A < #Aᣕᵃ

>
If Bob leaves the matrix,
then logic is violated.

That size must change with membership
can be abbreviated as 'WM.logic'.
The set of all and only WM.logical sizes
does not have a WM.logical size.
There is no first darkᵂᴹ WM.logical size,
so there is no darkᵂᴹ WM.logical size.
There is no size which flips between
being WM.logical and being WM.illogical.
Our sets do not change.
There are no negative.sized subsets of
the set of all and only WM.logical sizes,
so no WM.logical size is the size of
the set of all and only WM.logical sizes.
Nonetheless,
for each WM.logical size,
there is a larger.by.one WM.logical size.
Each.not.last is what permits Bob,
after all swaps,
to not.be.anywhere with a swap.in.
Do you (WM) demote the _set_ of
all and only WM.logical sizes
to the _collection_ of
all and only WM.logical sizes?
The swaps are still the swaps.
After all the swaps,
Bob is still not.being.anywhere with a swap.in.

If Bob leaves the matrix,
then logic is violated.
Therefore Bob cannot leave the matrix
in reasonable mathematics.

Not all sets obey WM.logic.

All your waffle cannot change this fact.

Eppur si muove.