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

joes formulated on Tuesday :

Am Tue, 29 Oct 2024 09:48:51 +0100 schrieb WM:

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.

Your claimed "dark numbers" may be interpreted as infinitesimal.

Not in the reals, but you should also consider that he started out with the dark naturals which also have no infinitesimals. He's only using the rationals and reals to confuse the issue. He wants some naturals to be so high and obscure in the clouds that they can't be (insert his daily favorite weasel word here) and hence Cantor was wrong to use them in his diagonal proof that the naturals and the rationals as sets have the same size.
His "dark numbers" may be interpreted as insanity.