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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Wed, 30 Oct 2024 13:34:08 -0700
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On 10/30/2024 1:19 PM, Moebius wrote:
> Am 30.10.2024 um 21:04 schrieb Chris M. Thomasson:
>> On 10/30/2024 12:48 PM, WM wrote:
>>> 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 ?
>>
>> 1/1 - 1/2 is greater than zero.
>>
>> Wow, what a discovery! lol. ;^/
>>
>> 1/2 - 1/3 is greater than zero.
>> 1/3 - 1/4 is greater than zero.
>> ... On and on ...
>>
>> They never hit zero. Got it?
>>
>> No unit [fraction] equals zero.
> 
> Yeah, that should be clear from the fact that an unit fraction has "the 
> form" 1/n where n is a natural number (by definition). Since there is no 
> natural number n such that 1/n = 0. :-P (If there were such a natural 
> number, say wm, we would get 1 = 1/wm * wm = 0 * wm = 0.)
> 
> Mückenheim's great discovery is that the DISTANCE between two "adjacent" 
> unit fractions is always > 0. Incredible!
> 
> For absolutely no reason he now "thinks" that this fact implies a 
> smallest unit fraction. :-)
> 

We know that the unit fractions tend to zero but never equal it. So, WM 
thinks well, the limit means finite? Or some shit like that? Humm...