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

Chris M. Thomasson wrote :

On 10/1/2024 6:28 AM, FromTheRafters wrote:

Chris M. Thomasson wrote :

On 9/30/2024 4:13 AM, Richard Damon wrote:

On 9/29/24 3:16 PM, WM wrote:

On 28.09.2024 14:58, Richard Damon wrote:

On 9/27/24 3:06 PM, WM wrote:

On 25.09.2024 19:12, Richard Damon wrote:
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The problem is that it turns out the NUF(x) NEVER actually "increments" by 0ne at any finite point, it jumps from 0 to infinity (Aleph_0) in the unboundedly small gap between 0 and all x

0,

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How do you distinguish them?

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They have different values, so why can't you?

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Then distinguish the first one.
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Regards, WM

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There isn't a first one.
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Show me a circle with 4 sides.

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;^) Humm, an n-gon where n is taken to infinity is a circle?

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As n goes to infinity, the angle of the vertices goes to 180 degrees -- is a straight line a circle?

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No. As n goes to infinity it makes a circle. Think of a finite view of a "large" number for n:
_________________________
n = 696969
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normal_base = 1.f / n;
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for (i = 0; i < n; ++i)
{
     normal = normal_base * i;
     angle = pi2 * normal;
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     p0 = { cos(angle), sin(angle) };
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     plot(p0);
}
_________________________
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I typed this in the newsreader, so sorry for any typos! This a finite view of a unit circle. Not a line.
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Take n to infinity, well, its a circle...
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Taking an n-gon to infinity is a circle.

 It is 'never' a circle.
 https://www.craig-wood.com/nick/articles/pi-archimedes/