Re: Replacement of Cardinality

Le 29/07/2024 à 20:33, Jim Burns a écrit :

On 7/29/2024 9:23 AM, WM wrote:

NUF(x) cannot grow by more than 1 at any x.

 NUF(x) = |⅟ℕ∩(0,x]|
NUF(x) cannot grow by more than 1 at any x > 0

Correct. At x < 0 or x = 0 NUF(x) = 0 and remains so.

¬(0 > 0)

Correct.

⅟ℕ∩(0,x] has
each non.{}.subset maximummed
each unit.fraction down.stepped
each non.maximum up.stepped
and therefore
ℵ₀.many unit.fractions
 x > 0  ⇒  NUF(x) = ℵ₀

That implies a growth between [0, 1] and (0, 1].
Between [0, 1] and (0, 1] NUF(x) cannot grow because no unit fraction fits in between.
Strange how void of logical thinking matheologians are.
Regards, WM