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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 7 Oct 2024 11:56:25 +0200
Message-ID: <ve0b89$3q71$2@solani.org>
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On 07.10.2024 11:38, FromTheRafters wrote:
> WM wrote :
>> On 06.10.2024 18:48, Alan Mackenzie wrote:

>>> You are getting confused with quantifiers, here.  For each such x, there
>>> is an infinite set of fractions less than x.  For different x's that set
>>> varies.  There is no such infinite set which appears before every x > 0.
>>
>> The set varies but infinitely many elements remain the same. A 
>> shrinking infinite set which remains infinite has an infinite core.
> 
> Wow, your shrinking sets again? Sets don't change.

There is a set-function, a set of sets. Every x that is closer to zero 
makes the set smaller, but never finite. Therefore the argument that the 
set varies but does not keep the same infinite core is stupid.

Regards, WM