Re: The set of necessary FISONs

On 1/26/2025 4:49 AM, WM wrote:

On 25.01.2025 21:23, Jim Burns wrote:

On 1/25/2025 2:35 PM, Jim Burns wrote:

On 1/25/2025 6:02 AM, WM wrote:

Swaps cannot eliminate Bob.
He remains but i the darkness.

>
A set larger than
any set with
⎛ fuller.by.one sets larger and
⎝ emptier.by.one sets smaller
is not
any set with
⎛ fuller.by.one sets larger and
⎝ emptier.by.one sets smaller.
>

No swaps are into the darkness.

>
No swaps can complete actual infinity of ℕ.

No actual infinity is represented by the first column.

No appendix 𝔻 such that ∀d ∈ 𝔻: f(d) = d
completes potential.infinity to actual.infinity.

No swaps can complete actual infinity of ℕ.

For each FISON, there is
a fuller.by.one FISON which is larger.
That is complete enough
in order to allow Bob to disappear.
Bob disappears where
a set emptier.by.Bob maps losslessly to
a set fuller.by.one,and
both sets, with without and with Bob,
are not any set with
⎛ fuller.by.one sets larger and
⎝ emptier.by.one sets smaller.
The sets aren't larger and aren't smaller.
They are the same size,
which allows Bob to disappear by lossless swaps.