Re: How many different unit fractions are lessorequal than all unit fractions? (repleteness)

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:

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Put pencil to paper and draw two curves which cross.
There is a point at which the curves intersect.

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This proves that no line has gaps.

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A point (hypothetically) next to 0
has an absence of points between it and 0
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No such absence of points exists.
No point which is next to 0 exists.
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Theorems or axioms?
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In the physics, think on your wave/particle duality,
and the extended body, for example the wave-packet.
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"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.
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... At a point, of for example where
they're incident, they coincide.
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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.
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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".
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What it declares is that "complementary duals" have
that the points and the space and the space and the
points are for each other.
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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:
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https://youtu.be/k9qpHcfiDho
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 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.