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

On 29.10.2024 09:36, joes wrote:

Am Mon, 28 Oct 2024 20:55:19 +0100 schrieb WM:

On 28.10.2024 12:21, Richard Damon wrote:

On 10/28/24 6:30 AM, WM wrote:

On 27.10.2024 18:05, Moebius wrote:

Am 27.10.2024 um 17:07 schrieb WM:
>

After NUF(x') = 1

There is no x' e IR such that NUF(x') = 1.

There is NUF(0) = 0. NUF(1) > 0. Hence NUF increases. This cannot
happen by more than single unitfractions with interruptions, according
to mathematics:
∀n ∈ ℕ: 1/n - 1/(n+1) > 0 .

It can not happen AT FINITE VALUES, but can "between" them,

Yes, at undefinable values.

Yes, they are infinitesimal.

There are no infinitesimal x > 0 on the real axis. But your claim may be interpreted as dark numbers x because they cannot be determined.

 

like just above 0, where it jumps from 0 to Aleph_0

Not at one point, definable or not.

Regards, WM