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

After serious thinking WM wrote :

On 01.11.2024 11:57, FromTheRafters wrote:

It happens that WM formulated :

On 01.11.2024 00:43, Richard Damon wrote:

On 10/31/24 1:35 PM, WM wrote:

On 31.10.2024 12:36, Richard Damon wrote:

On 10/30/24 11:38 AM, WM wrote:

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NUF(x) MUST jump from 0 to Aleph_0 at all real values x, as below ANY real number x, there are Aleph_0 unit fractions.

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You cannot distinguish them by any real number? That proves that they are dark.

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They are not finite values.

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All unit fractions are finite values.

 Each unit fraction is finite, the set of all unit fractions is not finite. Not finite is 'infinite' and there is no potential or actual anymore -- just finite and not finite.

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Actual means that all are there,

They are all there anyway, by definition.

including the smallest.

No smallest, since you simply inverted the set of naturals which has no largest.

Why?

Because you say so, I guess. Mathematicians don't think so. Taking finite subsets of the infinitely many ordered naturals gives you your first and last elements in any desired subsequence. Infinite subsets don't do that for you, even if you wish really hard.

It is a point on the real line, well separated from its neighbour.

No point on the real line is separated, that is for discrete sets.
https://mathworld.wolfram.com/DiscreteSet.html