Re: The non-existence of "dark numbers"

On 17.03.2025 16:50, Jim Burns wrote:

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.

You need not find out it but apply it.

 

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

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

 That's circular.

No, it is correct by definition of finite.

You won't or can't answer non.circularly.

In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. (Wikipedia)
That means it has a natural number of elements.

 

Then apply your version of "finite" and
answer at which finite index
the first loss in lossless exchange happens.

 After all swaps,

Nothing happens anymore.

No swap exists immediately before all the swaps.
No visibleᵂᴹ and no darkᵂᴹ.

Therefore: If Bob disappears, it happens at a finite index. Name it or confess that you have used a foolish idea.
Regards, WM