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

On 11/1/24 7:38 AM, 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.

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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.

 Actual means that all are there, including the smallest. Why? It is a point on the real line, well separated from its neighbour.
 

Only if there IS a "smallest".
Infinite sets do not need to have both ends in them.
The Greatest Lower Bound of the Unit Fractions is not a Unit Fraction, but 0, and thus there is no "smallest" unit fraction, so even in "Actual Infinity" there isn't one.
If you logic can't handle that, it can't handle actual infinity.

Regards, WM
 Regards, WM