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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Tue, 6 Aug 2024 03:55:05 +0200
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Am 06.08.2024 um 00:19 schrieb Jim Burns:
> On 8/5/2024 3:04 PM, WM wrote:

>> For every number of unit fractions
>> NUF(x) gives the smallest interval (0, x).

Huh?!

IIRC: NUF(x) := |{u ∈ ⅟ℕ : u < x}|  (x e IR)

Hence NUF(x) does NOT "give the smallest interval (0, x)", but the 
(cardinal) number of (the set of) unit fractions which are smaller than 
x (with x e IR).

Seems that Mückenheim is panicking.