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Le 18/07/2024 à 23:42, Jim Burns a écrit :
> On 7/18/2024 4:55 PM, WM wrote:

>> But if
>> for all points x > 0
>> there are ℵo smaller unit fractions,
>> then
>> for the interval (0, oo)
>> there are ℵo smaller unit fractions.
> 
> No.

Like Bob. No reason to continue.

> For each point x > 0
> there are
> step.down non.⅟⌈⅟x⌉.step.up well.ordered.by.>
> unit.fractions in (0,x] which,
> because
> step.down non.⅟⌈⅟x⌉.step.up well.ordered.by.>
> are ℵ₀.many.

Of all unit fractions left of any x > 0, ℵ₀ are the same, finitely 
many are different.
> 
> No unit fractions are smaller than (0,∞)

Right. That means Fritsches x are not all x.
> 
>> Or is there a point in (0, oo) which
>> is not an x > 0?
> 
> No, but
> there is no point x in (0,∞) such that

irrelevant. All x > 0 are there and nothing else.

Regards, WM