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From: WM <wolfgang.mueckenheim@tha.de>
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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