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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Tue, 3 Sep 2024 12:22:19 +0200
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On 03.09.2024 06:25, Jim Burns wrote:
> On 9/2/2024 4:37 PM, WM wrote:
>> On 02.09.2024 19:19, Richard Damon wrote:
> 
>>> as any unit fraction you might claim to be
>>> that one has a unit fraction smaller than itself,
>>> so it wasn't the smallest.
>>
>> Your argument stems from visible unit fractions
>> but becomes invalid in the dark domain.
> 
> The darkᵂᴹ domain
>   between 0 and visibleᵂᴹ unit.fractions
> is empty.

Then you could see the smallest unit fraction. Remember that they are 
fixed points with non-empty gaps on the real line. Hence there is a 
first one.
> 
> Each positive point is undercut by
> visibleᵂᴹ unit.fractions,

No. Only each visible positive point is undercut by
visible unit.fractions.

> ⎛ Assume otherwise.

Assume that there is no first unit fraction. The alternative would be 
more first unit fractions, i.e., real nonsense.

>> The unit fractions end before zero.
> 
> The lower.end of unit fractions
> is not.

Then NUF(x) would remain at 0. It does not.

Regards, WM
> 
> 
>