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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (repleteness)
Date: Fri, 20 Sep 2024 20:02:57 -0700
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On 9/20/2024 7:42 PM, Ross Finlayson wrote:
> On 09/20/2024 02:38 PM, Chris M. Thomasson wrote:
>> On 9/20/2024 2:20 PM, Ross Finlayson wrote:
>>> On 09/20/2024 02:15 PM, Ross Finlayson wrote:
>>>> On 09/20/2024 12:26 PM, Jim Burns wrote:
>>>>> On 9/20/2024 2:10 PM, WM wrote:
>>>>>> On 20.09.2024 19:51, Jim Burns wrote:
>>>>>
>>>>>>> Put pencil to paper and draw two curves which cross.
>>>>>>> There is a point at which the curves intersect.
>>>>>>
>>>>>> This proves that no line has gaps.
>>>>>
>>>>> A point (hypothetically) next to 0
>>>>> has an absence of points between it and 0
>>>>>
>>>>> No such absence of points exists.
>>>>> No point which is next to 0 exists.
>>>>>
>>>>>
>>>>
>>>> Theorems or axioms?
>>>>
>>>> In the physics, think on your wave/particle duality,
>>>> and the extended body, for example the wave-packet.
>>>>
>>>> "Drawing" a line, "tire en regle", or curve,
>>>> has that when you put pencil to paper,
>>>> and draw a line, or curve if you will,
>>>> and life the pencil and put it back down,
>>>> and draw another one, intersecting the first:
>>>> the _curves_ cross.
>>>>
>>>> ... At a point, of for example where
>>>> they're incident, they coincide.
>>>>
>>>>
>>>> Then these lines-reals these iota-values
>>>> are about the only "standard infinitesimals"
>>>> there are: with extent you observe, density
>>>> you observe, least-upper-bound as trivial,
>>>> and measure as assigned, length assignment.
>>>>
>>>>
>>>
>>> Consider for example minutes between 1:00 and 3:00
>>> in this https://www.youtube.com/watch?v=fIexFF91Jl8
>>> "Moment and Motion:  medical imaging technology".
>>>
>>> What it declares is that "complementary duals" have
>>> that the points and the space and the space and the
>>> points are for each other.
>>>
>>>
>>
>> Actually, each frame in this is part of a 3d process for constructing a
>> volume that can be used in a volumetric renderer. It is close to medical
>> imaging wrt DICOM:
>>
>> https://youtu.be/k9qpHcfiDho
>>
>>
>>
> 
> I sure had a head cold that day.
> 
> Studying medical imaging that way was kind
> of totem-ish, like, maybe if I study medical
> imaging today, then sympathetic magic will
> help kick my cold and diseases begin with 'C'.
> Seemed helped, .... Yet, that's humor for you.
> 
> 
> About "points-in-a-line", the classical notion
> is "beads-on-a-string", here as with regards
> to "the course-of-passage", that ordinals have
> a course of passage through ordinals, and that
> line-drawing, has a course of passage through
> points.
[...]

Sure. Well, wrt beads on a string, check this out:

https://youtu.be/-PUmt7i3zw4

Feel free to look around. It's a 360.

:^) Each field line is comprised of tangent spheres. Now, the algorithm 
for n beads on a line is not all that difficult. Humm... Perhaps I 
should start a new thread with some examples and renders.