Re: how

Le 30/05/2024 à 22:24, Jim Burns a écrit :

NUF(x) = 1 between x = 0 and x = 1/10​^10​^10​^100000.

 No, NUF(x) ≠ 1

That would imply that not between all unit fractions distances existed. Therefore it is wrong.

 | Assume you are correct.
| Assume NUF(x) = 1  for
| 0 < x < 1/10​^10​^10​^100000.
|
| unit fraction ⅟n exists: 0 < ⅟n < x
| no unit fraction exists between 0 and ⅟n
|
| However,
| unit fraction ⅟(n+1) exists: 0 < ⅟(n+1) < ⅟n
| Contradiction.

Yes, if all n had successors, there would be a contradiction.
But it would not go away by your conclusion.

 Therefore, NUF(x) ≠ 1

And you are satisfied and don't see the contradiction?
 

After more definitions and more not.first.false claims,
we get to disappearances of Bob and so forth.

And you are satisfied and don't see the contradiction?

 

if your chain contains only correct conclusions, then your start must be wrong.

 Either one of EAX is wrong
⎛ E. The empty set ∅ exists.
⎜ A. For sets x and y, adjunct x⨭y = x∪{y} exists.
⎝ X. Two equi.membered sets are equal sets.
 or you are wrong.

Ask colleagues (without pointing to our discussion) whether they agree that in the course of exchanging elements, infinitely many elements can disappear. Ask further whether in the accumulation point of the sequence (1/n) infinitely many unit fractions can populate one and the same point.
Regards, WM