Re: Replacement of Cardinality

On 8/7/2024 1:47 PM, WM wrote:

Le 07/08/2024 à 19:07, Jim Burns a écrit :

We agree that
saying "INVNUF(3.5)" doesn't prove
INVNUF(3.5) exists
>
It is equally true that
saying "INVNUF(3)" doesn't prove
INVNUF(3) exists

>
Correct.
>

But we have
proof INVNUF(3) does not exist.

>
We have proof that INVNUF(3) exists.
∀n ∈ ℕ: 1/n - 1/(n+1) > 0 .
Why do you not consider this argument?

∀n ∈ ℕ:  ⅟n - ⅟(n+1)  >
⅟(n+1) - ⅟(n+2)  >
⅟(n+2) - ⅟(n+3)  >
⅟(n+3) - ⅟(n+4)  >  0
⅟n ≠ INVNUF(3)
The only part of your argument which you've shared is
∀n ∈ ℕ: 1/n - 1/(n+1) > 0
It seems likely that you're using
an unreliable quantifier shift
(which doesn't become reliable by staying implicit),
but
you (WM) find silence with regard to
the rest of your argument
more advantageous, apparently.
Your silence suggest that
you also find your argument unpersuasive.
Perhaps there is hope for you.