Re: how

Le 17/05/2024 à 21:08, Jim Burns a écrit :

On 5/17/2024 10:08 AM, WM wrote:

Le 17/05/2024 à 02:21, Jim Burns a écrit :

On 5/16/2024 7:00 PM, Moebius wrote:

Am 16.05.2024 um 20:56 schrieb Jim Burns:

On 5/15/2024 9:12 AM, WM wrote:

Between each pair of unit fractions,
there is a finite distance.

 Before each unit fraction ⅟n,
there is a smaller unit fraction ⅟(n+1).

These two conditions cannot be satisfied simultaneously.

 Each unit fraction is not first.
The unit.fraction.subset of the real line
does NOT have a first element.

This condition violates this condition:

 

To gather ℵ₀ unit fractions,
ℵ₀ finite distances are required.

Their sum is not zero.

 The greatest lower bound of d > 0 is 0
which does NOT contradict |(x,x+d)| ≮ ℵ₀

It contradicts this: To gather ℵ₀ unit fractions, ℵ₀ finite distances are required. And even this one: To gather two unit fractions, a finite distance is required.

 

Therefore the statement
NUF(x) = ℵ₀ für x > 0
is wrong.

Please let me know where your claimed ℵ₀ first unit fractions sit. The interval is (0, ?). Please fill in. Otherwise your claims are counterfactual.
Regards, WM