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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 9 Sep 2024 11:49:41 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Mon, 09 Sep 2024 12:27:47 +0200 schrieb WM:
> On 08.09.2024 22:11, Richard Damon wrote:
>> On 9/8/24 3:48 PM, WM wrote:
> 
>>> Select any gap between one of the first ℵo unit fractions and its
>>> neighbour. Call its size x. Then ℵo unit fractions cannot fit into the
>>> interval (0, x), independent of the actual size.
>> But that is changing the value of x in the middle of the problem which
>> isn't allowed.
>> Given that new x, we can choose a new set of Aleph_0 unit fractions
>> below that x.
> ℵo unit fractions are claimed to be smaller than every x > 0. If that is
> true then I can choose as the x one of the ℵo intervals between two of
> them.
More precisely: every positive x has infinitely many smaller unit
fractions (mind the quantifier order). A number is not an interval.

-- 
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.