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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Wed, 30 Oct 2024 21:19:17 +0100
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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. :-)