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

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".
 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