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

Am Sat, 07 Sep 2024 15:06:08 +0200 schrieb WM:

On 07.09.2024 04:01, Richard Damon wrote:

On 9/6/24 8:07 AM, WM wrote:

 

NUF(x) must grow. It cannot grow by more than 1 at any x.

Only if it exists.

There is no reason to deny its existence. If there is zero and all real
numbers x > 0 and if there are unit fractions, then we can ask how many
unit fractions are between 0 and any x.

You seem to be denying the existence of an infinite step function
(regardless of whether you believe it to be equal to yours). You are
imagining function that somehow (looking from the right) counts down
infinity going to the left. I understand your argument of unique single-
step positions, yet there is no space for an infinity of them.

If it does, it must be counting some sub-finite values as "unit
fractions" that are not the reciprocal of the Natural Numbers

Only reciprocals of natural numbers are counted.

Which are all visible/definable/light/finite.

 > (since there is no smallest of those unit fractions to count from).
Perhaps you consider only definable natural numbers. They have no
largest element.

Thank you.

[fix your quotes]

Maybe that is your dark numbers, these sub-finite numbers that are
reciprocals of some post-finite values above the infinite set of
Natural Numbers (which have no upper bound) and are below Omega.

Dark numbers are post finitely definable.

Uh what now?

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.