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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: quantifier order
Date: Mon, 9 Sep 2024 19:55:41 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <2e31239990bdcbe4ce41a3b9a2e17859d4c3e438@i2pn2.org>
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Am Mon, 09 Sep 2024 21:03:24 +0200 schrieb WM:
> On 09.09.2024 17:49, joes wrote:
>> Am Mon, 09 Sep 2024 17:32:11 +0200 schrieb WM:
>>> On 09.09.2024 17:15, joes wrote:
>>>> Am Mon, 09 Sep 2024 16:53:32 +0200 schrieb WM:
>>>
>>>>> You claim that ℵo unit fractions are smaller than ANY x > 0.
>>>> Yes. Not all the same ones of course.
>>> My question concerns same unit fractions only. Do ℵo unit fractions
>>> exist smaller than any x > 0? If not, how many same unit fractions
>>> exist smaller than any x > 0? How many are smalleror equal than all
>>> unit fractions?
>> That is a different question
> No, that is THE question.
The set of unit fractions smaller than all x is empty.
However, the set of UFs smaller than one arbitrary x is infinite.

>> Of course no unit fraction is smaller than every other unit fraction.
-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.