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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Thu, 12 Sep 2024 14:15:15 -0400
Organization: i2pn2 (i2pn.org)
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On 9/12/24 1:48 PM, WM wrote:
> 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.

So, you are admitting that your "Dark Numbers" are just caused by your 
having insufficent intelegence to understand the true nature of the 
actual Natural Number System.


>>
>>> 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.

Right, and that includes the space between the point you think is the 
first point of the open interval and the end point of that interval 
(which is outside the interval) proving that your point wasn't the first 
there.

> 
> Regards, WM
>