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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: quantifier order
Date: Tue, 10 Sep 2024 18:24:25 +0200
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On 09.09.2024 21:55, joes wrote:
> Am Mon, 09 Sep 2024 21:03:24 +0200 schrieb WM:
>> On 09.09.2024 17:49, joes wrote:

>> No, that is THE question.
> The set of unit fractions smaller than all x is empty.

Why is this so? Because all unit fractions are undercut by some x. The x 
undercutting the last unit fractions (you said that none remains because 
the set is empty, therefore all must be gone) do not satisfy your 
following claim:

> However, the set of UFs smaller than one arbitrary x is infinite.
Regards, WM