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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: Sat, 5 Oct 2024 22:51:08 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <08047fe749f5eb9e923344e444f7acaa419416e4@i2pn2.org>
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On 10/5/24 2:58 PM, WM wrote:
> On 05.10.2024 15:28, Richard Damon wrote:
>> On 10/5/24 8:15 AM, WM wrote:
>>> On 05.10.2024 13:01, Richard Damon wrote:
>>>> On 10/5/24 5:18 AM, WM wrote:
>>>>> On 05.10.2024 00:45, Richard Damon wrote:
>>>
>>>>>> Nope, and that is your problem, that property only hold at both 
>>>>>> ends for finite sets.
>>>>>
>>>>> Every point is a finite set.
>>>>>
>>>> And the set of *A* point has no "next" point, as it is just one.
>>>
>>> But it has a position, like the point 1/3 - if it is not dark.
>>> By the way: Also a pair of points is a finite set. And it has a gap 
>>> and every member has a next point.
> 
>> So why does that say it has a point next to it?
> 
> A point between both could be chosen unless it was dark.
> 
> Regards, WM
> 

And that point CAN be found, Given two point x and y, there is a point 
(x+y)/2 between them, so they could not have been "next" to each other,

The fact that we can keep doing that indefinitely, and never reach a 
point we can't continue, is proof that the concept of "next point" 
doesn't exist, except in your broken logic that actually doesn't 
actually have real infinte sets even though your erroneously try to call 
it actual infinity.