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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Tue, 29 Oct 2024 09:48:51 +0100
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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