Re: how

On 6/13/2024 3:48 AM, WM wrote:

Le 12/06/2024 à 23:04, "Chris M. Thomasson" a écrit :

On 6/12/2024 2:03 PM, Chris M. Thomasson wrote:

On 6/12/2024 1:58 PM, WM wrote:

Le 12/06/2024 à 22:51, "Chris M. Thomasson" a écrit :

On 6/12/2024 1:38 PM, WM wrote:

>
Yes, it is impossible to find a last one before ω.

>
Indeed. You are correct here. There is no last dark number?

>
There is one (think of the first unit fraction) but as it is and remains dark, it cannot be caught.

>
I thought there were infinitely many dark natural numbers? If so, how can there possibly be a largest dark number?
>

>
You told me that there are indeed infinitely many dark natural numbers, right?
>

Yes. You cannot get to the end because dark numbers have no discernible order.
 Fact is: If we assume the existence of ω at the ordinal line, then something must exist before, either dark numbers or nothing. There is no third alternative. Or can you imagine one?

Let be imagine something that was dark:
A = 1024^42426969
B = A + 1
A and B were already in the set of natural numbers, right?