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From: Python <python@invalid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Fri, 6 Sep 2024 00:36:51 +0200
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Le 05/09/2024 à 22:44, crank Wolfgang Mückenheim, aka WM a écrit :
> On 05.09.2024 20:56, Jim Burns wrote:
>> On 9/5/2024 9:53 AM, WM wrote:
> 
>> Insisting that ω-1 exists and that,
>> for b ≠ 0 and β < ω, β-1 exists
>> is
>> insisting that ω is finite.
> 
> No.
>>
>> The most frugal explanation of your claim is that
>> you simply do not know what 'finite' means.
> 
> Finite means that you can count from one end to the other. Infinite 
> means that it is impossible to count from one end to the other.
> 
>>> Do you believe that it needs a shift to state:
>>> All different unit fractions are different.
>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
>>> I can see no shift.
>>
>> It needs a shift to conclude from
>> ( for each ⅟j: there is ⅟k≠⅟j: ⅟k < ⅟j
>> that
>> ( there is ⅟k: for each ⅟j≠⅟k: ⅟k < ⅟j
>>
>> Have you evolved on that topic?
> 
> You are mistaken. I do not conclude the latter from the former. I 
> conclude the latter from the fact that NUF(0) = 0 and NUF(x>0) > 0 and 
> never, at no x, NUF can increase by more than 1.

What the Hell could mean "to increase at an x" ?