Re: Replacement of Cardinality

On 8/27/24 3:36 PM, WM wrote:

Le 26/08/2024 à 02:15, Moebius a écrit :

Am 25.08.2024 um 23:18 schrieb Jim Burns:

On 8/25/2024 3:35 PM, WM wrote:

>

Dark numbers are not any bounds.

>
Fascinating: So we have that there are "dark numbers" which are smaller (larger) than each and every s e SB (n e IN), but they are no bounds?

 Dark natural numbers are larger than any visible natural number but smaller than their bound omega.
Dark unit fractions are smaller than any visible unit fractions but larger than their bound 0.
 Regards, WM
 

And since the upper bound of the "visible" natural numebers is omega, since every visible natural number MUST be followed by the next Natural Number (since there isn't a definable maximum visible number, since given a visible number, we can always add one to it) and the lower bound of the "visible" unit fractions is 0, as any larger finite bound allows the creation of a smaller unit fraction below it.
So, your "dark numbers" are squeezed out of the finite number space into some "beyond-finite" number space.
Perhaps something like the hyper-reals.