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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: Thu, 12 Sep 2024 19:48:56 +0200
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On 12.09.2024 14:29, FromTheRafters wrote:
> After serious thinking WM wrote :
>> Le 11/09/2024 à 23:13, FromTheRafters a écrit :
>>> Chris M. Thomasson laid this down on his screen :
>>>> On 9/11/2024 12:40 PM, WM wrote:
>>
>>>>> Open intervals are intervals which have dark endpoints.
>>>>
>>>> What about the gray ones?
>>>>
>> Grey points are dark points which can become visible.
> 
> Points which change? What function causes a point to change?

For an eartworm all numbers are dark, for a dove numbers 1 to 7 are 
visible, for your pocket calculator numbers 1 to 10^99 are visible. If 
you couple some calculators, you get farther.
> 
>> But the endpoints of open intervals will remain dark forever.
> 
> Open intervals simply don't contain endpoints, dark or otherwise.

You simply don't know about them. No spot of an interval is free of 
points. No point of an interval is free of points.

Regards, WM