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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Thu, 31 Oct 2024 07:00:52 -0400
Organization: Peripheral Visions
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on 10/31/2024, WM supposed :
> On 31.10.2024 10:04, FromTheRafters wrote:
>> WM wrote :
>>> On 31.10.2024 09:29, FromTheRafters wrote:
>>>> WM submitted this idea :
>>>>> On 30.10.2024 21:24, FromTheRafters wrote:
>>>>>> WM explained :
>>>>>>> On 30.10.2024 16:43, FromTheRafters wrote:
>>>>>>>> on 10/30/2024, WM supposed :
>>>>>>>
>>>>>>>>> Believe what you like without foundation.
>>>>>>>>> If ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 is true, the NUF(x) grows in steps of 
>>>>>>>>> not more than 1.
>>>>>>>>
>>>>>>>> Wrong.
>>>>>>>
>>>>>>> What? ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 ?
>>>>>>
>>>>>> No, the other part. Your 'conclusion' is a non sequitur.
>>>>>
>>>>> My conclusion is that all unit fractions are separated by large sets of 
>>>>> real points from each other. Never two or more unit fractions are at the 
>>>>> same point. Is that what you doubt? Hardly.
>>>>>
>>>>> Then you must doubt that NUF(x) can grow only by 1 at any point x? But 
>>>>> why?
>>>>
>>>> Because NUF() doesn't "grow" it just *is*.
>>>
>>> According to set theory every function just "is". But we analyze or 
>>> describe its behaviour with increasing argument x as increasing, constant 
>>> or decreasing. Should that be forbidden in case of NUF in order to avoid 
>>> problems?
>> 
>> Well, it would cure your discontinuity dyslexia problems.
>
> No mathematical arguments available?
> No mathematical arguments available!

Failure to recognize that discontinuity is mathematical noted.