Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions?
Date: Tue, 08 Oct 2024 06:50:50 -0400
Organization: Peripheral Visions
Lines: 40
Message-ID: <ve32qf$25lne$1@dont-email.me>
References: <vb4rde$22fb4$2@solani.org> <vdr1g3$n3li$6@dont-email.me> <8ce3fac3a0c92d85c72fec966d424548baebe5af@i2pn2.org> <vdrd5q$sn2$2@news.muc.de> <55cbb075e2f793e3c52f55af73c82c61d2ce8d44@i2pn2.org> <vdrgka$sn2$3@news.muc.de> <vds38v$1ih6$6@solani.org> <vdscnj$235p$1@news.muc.de> <vdtt15$16hg6$4@dont-email.me> <vdu54i$271t$1@news.muc.de> <vduata$19d4m$1@dont-email.me> <vduf0m$1tif$1@news.muc.de> <ve076s$1kopi$2@dont-email.me> <ve0j4r$1eu7$2@news.muc.de> <ve2rlh$24f8f$2@dont-email.me> <ve302i$ggk$2@news.muc.de> <ve326r$24i4i$7@dont-email.me>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="iso-8859-15"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 08 Oct 2024 12:50:56 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="183e3fa38b53451b283b297c8ebb227e";
	logging-data="2283246"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+vs8o9bo42zn9LW0uDBjaOrGj72BQWyVg="
Cancel-Lock: sha1:nCR5FJozWs8d0tRgpVf6pOjqLFg=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376
Bytes: 3062

WM wrote on 10/8/2024 :
> On 08.10.2024 12:04, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>
>>> All unit fractions are points with uncounably many points between each
>>> pair.
>> 
>> Yes, OK.
>> 
>>> Hence all must be visible including the point next to zero, but they
>>> are not.
>> 
>> There is no point next to zero.
>
> Points either are or are not. The points that are include one point next to 
> zero.
>>>>> A shrinking infinite set which remains infinite has an infinite core.
>> 
>>>> Again, no.  There is no such thing as a "core", here.  Each of these sets
>>>> has an infinitude of elements.  No element is in all of these sets.
>> 
>>> Try to think better. A function of sets which are losing some elements
>>> but remain infinite, have the same infinite core.
>> 
>> That is untrue.  For any element which you assert is in the "core", I
>> can give one of these sets which does not contain that element.
>
> Of course, the core is dark.
>
>>  The
>> "core" is thus empty.
>
> The infinite sets contain what? No natural numbers? Natural numbers dancing 
> around, sometimes being in a set, sometimes not? An empty intersection 
> requires that the infinite sets have different elements.

An infinite intersection requires that all elements are in each set. 
The intersection is empty because not all elements are in every set. 
Each successive set in your sequence of sets removes another element 
from consideration - until they are all gone.