Re: The non-existence of "dark numbers"

On 3/17/2025 12:58 AM, WM wrote:

On 17.03.2025 05:23, Jim Burns wrote:

On 3/16/2025 6:22 PM, WM wrote:

On 16.03.2025 20:41, Jim Burns wrote:

On 3/16/2025 3:27 PM, WM wrote:

The question here is
the index of the first disappearance of Bob.

>
The answer requires you to know what 'finite' means.

>
Answer using your definition of
finite index or finite natural number.

>
You misunderstand.
I don't need to find out what 'finite' means.

Do you (WM) know what 'finite' means?

>
Yes, it means the index is a natural number.

That's circular. Again.
You won't or can't answer non.circularly.
Would you (WM) like to know what 'finite' means?
Not merely trade 'finite' for a different word?
https://en.wikipedia.org/wiki/Finite_set

Then apply your [not.WM] version of "finite" and
answer at which finite index
the first loss in lossless exchange happens.

After all swaps,
the matrix holds only numbers originally in
the same.sized first column.
No swap exists immediately before all the swaps.
No visibleᵂᴹ and no darkᵂᴹ.
----
For each set A to which WM.logic applies,
WM.logic applies to fuller.by.one Aᣕᵃ.
WM.logic A  ⇒  WM.logic Aᣕᵃ
For each set A to which WM.logic applies,
Aᣕᵃ is larger.
WM.logic A  ⇒  #A < #Aᣕᵃ
{#C:WM.logic.C} is the set of sizes #A of
sets A to which WM.logic applies.
WM.logic does not apply to {#C:WM.logic.C}
Not WM.logic {#C:WM.logic.C}
⎛ Assume otherwise.
⎜ Assume your logic applies to {#C:WM.logic.C}
⎜ WM.logic {#C:WM.logic.C}
⎜
⎜ The size #{#C:WM.logic.C} is in {#C:WM.logic.C}
⎜ #{#C:WM.logic.C} = 𝔊
⎜ 𝔊 ∈ {#C:WM.logic.C}
⎜
⎜ {#C:#C≤𝔊+1} is a set of set.sizes,
⎜ each of which your logic applies to,
⎜ each of which is in {#C:WM.logic.C}
⎜ {#C:#C≤𝔊+1} ⊆ {#C:WM.logic.C}
⎜
⎜ However,
⎜ {#C:#C≤G+1} is larger than {#C:WM.logic.C}
⎜ A subset can't be larger.
⎝ Contradiction.
Therefore,
your logic does not apply to
the set of sizes of
sets to which your logic applies.
not WM.logic {#C:WM.logic.C}