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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Thu, 8 Aug 2024 00:17:09 +0200
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Am 07.08.2024 um 23:29 schrieb Jim Burns:
> On 8/7/2024 3:01 PM, WM wrote:
>> Le 07/08/2024 à 20:29, Jim Burns a écrit :
> 
>>> The only part of your argument which you've shared is
>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
>>
>> That is the decisive part.

Actually, his "thinking process" is simple:

"Since there is a gap (space) between adjacent unit fractions and all 
unit fractions are in the interval (0, 1], there must be FINITELY MANY 
of them (i.e. a first/smallest one)." (Don't ask! At least this 
"argument" seems to be CLEAR FOR HIM).

And of course, in this case:

>> Never two or more unit fractions are added to NUF [starting with NUF(0) = 0].

Right. And if x1 e IR is "the position" of the first/smallest unit 
fraction, then NUF(x1) = 1.

>>> you (WM) find silence with regard to
>>> the rest of your argument
>>> more advantageous, apparently.
>>
>> There is no rest.

Right!

I mean, it's an OBVIOUS FACT (in Mückenheim's world).