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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?
Date: Sat, 7 Sep 2024 15:08:38 +0200
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On 07.09.2024 04:01, Richard Damon wrote:
> On 9/6/24 4:40 PM, WM wrote:
>> On 06.09.2024 14:38, joes wrote:
>>> Am Fri, 06 Sep 2024 14:12:29 +0200 schrieb WM:
>>
>>>>> 0 < ... < ⅟⌊4+⅟x⌋ < ⅟⌊3+⅟x⌋ < ⅟⌊2+⅟x⌋ < ⅟⌊1+⅟x⌋ < x
>>>> 0 is smaller than all that. Therefore there is no increase at 0.
>>>> x is larger than all that. Therefore your x is not the least one
>>>> posiible.
>>> Therefore no x can be the least unit fraction.
>>
>> No definable x. No epsilon.
> 
> Which means no "Unit Fraction" as the reciprical of a Natural Number, 
> since they are all definable.

All natural numbers which you recognize are definable.
> 
> Thus, your NUF must also be counting some sub-finite values, or it just 
> doesn't exist.

It exists. It counts definable numbers as well as sub-finitely definale 
numbers.

Regards, WM