Re: The non-existence of "dark numbers"

On 19.03.2025 16:18, Jim Burns wrote:

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

⎛ Bob is in.matrix before.swaps, but
⎝ Bob is NOT in.matrix after.swaps.

Then he must have left by a swap or by a miracle of matheology. I do not accept the latter, ad I can prove that the former is in contradiction to logic.>

After all the swaps,
without ever disappearing into
anywhere other than a finitec 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.

 

If there is an "after all swaps",
then all O have settled within the matrix.

 That matrix,
with rows and columns indexed by
the emptiest inductive set,
after all the swaps,
that matrix doesn't hold any O.

That is wrong because O cannot get lost. The O remain but at dark places.

 ⎛ Assume otherwise.
⎜ Assume that it's after all swaps,
⎜ and O is in cell <k,1>

That's the first mistake. All O's are in dark cells which cannot be distinguished.

After all the swaps,
Bob is lost from all finite indices.

>
No, that is impossible.
Here lies your mistake.
The matrix has no drain!

 If the set of
all set.sizes needing a drain
is a set of a size needing a drain,
then
that set has subsets larger than it, the set.
 

That is impossible. Therefore dark numbers must be accepted.
Regards, WM