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

On 9/10/2024 1:38 PM, Moebius wrote:

Am 10.09.2024 um 22:33 schrieb Chris M. Thomasson:

On 9/10/2024 12:30 PM, Moebius wrote:

Am 10.09.2024 um 20:38 schrieb Chris M. Thomasson:

On 9/10/2024 11:35 AM, Chris M. Thomasson wrote:

On 9/9/2024 5:32 PM, Moebius wrote:

Am 10.09.2024 um 01:08 schrieb Chris M. Thomasson:
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Take the gap between:
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1/1 and 1/2. There are infinitely many unit fractions that are small enough to fit within that gap.

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Oh, really?! Could you name (just) o n e? :-)

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1/4?

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1/4 is between 1/1 and 1/2:
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1/1---->1/4---->1/2

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lol. If you say so. :-)
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So, it's not _strict_

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Actually, it's not between 1/2 and 1/1 at all (if we presuppose the usual order < on the rational numbers).

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The LENGTH OF THE gap from 1/1 to 1/2 is 1/2 so there are infinity many unit fractions that are smaller than 1/2.

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MAN, YOUR ORIGINAL CLAIM WAS: "1/4 is between 1/1 and 1/2."
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THIS CLAIM IS WRONG. (WRONG! WORONG!)
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FUCK YOUR "GAP".
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Please don't do the Mückenheim her. One crank is enough.

 1/4 is smaller than the gap. Think of a normalized gap:
 To normalize the distance between two points in n-ary space. p0 and p1 can be n-ary vectors.
 p0 = 1/2
p1 = 1/1
pdif = p1 - p0
 the mid point would use the unit fraction 1/2 at:
 pmid = p0 + pdif * 1/2
 right?
 this means there are infinite unit fractions that can be used for the gap. The line from p0 to p1?