Re: Replacement of Cardinality

On 8/6/24 4:35 AM, WM wrote:

Le 06/08/2024 à 00:35, Jim Burns a écrit :

On 8/5/2024 3:21 PM, WM wrote:

Le 05/08/2024 à 02:24, Moebius a écrit :

>

∃^ℵ₀ u ∈ ⅟ℕ: ∀x > 0: u < x   (false) .

>
∃^NUF(x) u ∈ ⅟ℕ: ∀x > 0: u < x true.

>
¬∃u ∈ ⅟ℕ: ∀x > 0: u < x

 Right. But with NUF(x) = 1 ==> INVNUF(1) = x we get
 ∃u ∈ ⅟ℕ, u < x, ∀y > x = INVNUF(1).
 Regards, WM
 

But INVNUF(1) can't exist, as it will be bigger than
1/ ( ceil(1/INVNUF(1)) +1 ), and 1/ ( ceil(1/INVNUF(1)) +2 )
which are two different unit fractions.
And thus proving that it can't exist.