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NNTP-Posting-Date: Fri, 20 Sep 2024 21:15:33 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (repleteness)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Fri, 20 Sep 2024 14:15:26 -0700
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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.