Re: Replacement of Cardinality

On 8/7/2024 2:51 PM, WM wrote:

Le 07/08/2024 à 20:03, Jim Burns a écrit :

On 8/7/2024 8:31 AM, WM wrote:

Do you agree that
all unit fractions with no exception
have gaps on the real line?

>
Each unit fraction ⅟n has,
for n ≠ 1, a gap between ⅟n and ⅟(n-1)
a gap between ⅟n and ⅟(n+1)  and
a gap between ⅟(n+1) and ⅟(n+2)
thus

>
Never more than one unit fraction
can be added simultaneously to NUF(x).

⅟n and ⅟(n+1) and ⅟(n+2) aren't
simultaneous [colocated]
NUF(⅟n) > 1
⅟n ≠ INNUF(1)
Each unit fraction ⅟n ≠ INVNUF(1)
Finite doesn't need to be small.
Finite can be big compared to Avogadroᴬᵛᵒᵍᵃᵈʳᵒ
and, if it shares finiteness.properties with 1
and with Avogadroᴬᵛᵒᵍᵃᵈʳᵒ, it is finite.
Infinite is beyond all finites, even big.finites.
Infinite does not have finiteness.properties.