Sujet : Re: Replacement of Cardinality
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.logic sci.mathDate : 07. Aug 2024, 19:03:55
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <dc6ab75f-e7fd-4e39-83a7-2a04c4155d21@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 8/7/2024 8:31 AM, WM wrote:
Le 06/08/2024 à 18:33, Jim Burns a écrit :
On 8/6/2024 9:55 AM, WM wrote:
Le 06/08/2024 à 14:38, Jim Burns a écrit :
NUF(x) ≠ 1
is true everywhere
NUF(x) = 1 ⇒ INVNUF(1) = x
is true everywhere
However,
its truth doesn't imply INVNUF(1) exists.
>
∀n ∈ ℕ: 1/n - 1/(n+1) > 0
implies its existence.
>
No.
∀n ∈ ℕ: 1/n - 1/(n+1) > 0
implies its NONexistence.
>
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
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.