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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 20:00:17 -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.
> 
> Divising a specialization of "in", "on", and
> "about", the line, its points, helps to characterize
> that line-drawing makes points "in" a line, that
> zooming in via field operations points to, that
> it establishes a vector field with all the arrows
> reducing in region until their heads touch and
> that they point-to, a point, "on" a line, then
> as with regards to a super-fine comb each tooth
> "about" the line.
> 
> DICOM is a family of standards in medical imaging
> data and metadata, sort of like JPEG for doctors.
> See also "HL7". The JPEG2000 is pretty great,
> I studied data formats a lot.

A single DICOM file can contain the image stack that its based on, 
right? Fwiw, here is a render of some of my experiments:

https://www.facebook.com/photo/?fbid=334035991088739&set=a.110008616824812

A screenshot:

https://i.ibb.co/jGjycbN/image.png

Strange results for sure.


> 
> 
> Chaos theory and its terms is sort of folded into
> "dynamical modeling", as with regards to for example
> "limit cycles" for "attractors", then as with regards
> to for example Nayfeh's tome on non-linear oscillations.
> 
> 
> Anyways, here line-reals and signal-reals "exist"
> next to field-reals, at least three models of
> continuous domains, each with their own definition
> of "continuous", all satisfying the same properties
> of extent, density, completeness, and measure, from
> which can be established most all their combined
> character, as "real-valued".
> 
> 
>