Path: ...!Xl.tags.giganews.com!local-1.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 07 Oct 2024 23:44:21 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Newsgroups: sci.math
References: <vb4rde$22fb4$2@solani.org> <vdrd5q$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> <RJKcnSeCMNokRpz6nZ2dnZfqnPadnZ2d@giganews.com>
 <vdto2k$1jte$1@news.muc.de> <vdu4mt$18h8h$1@dont-email.me>
 <vdu874$271t$2@news.muc.de> <vdua6f$18vqi$2@dont-email.me>
 <vdubg3$24me$1@news.muc.de> <4bc3b086-247a-4547-89cc-1d47f502659d@tha.de>
 <ve0n4i$1vps$1@news.muc.de> <ve10qb$1p7ge$1@dont-email.me>
 <ve117p$vob$1@news.muc.de>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Mon, 7 Oct 2024 16:44:32 -0700
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101
 Thunderbird/38.6.0
MIME-Version: 1.0
In-Reply-To: <ve117p$vob$1@news.muc.de>
Content-Type: text/plain; charset=windows-1252; format=flowed
Content-Transfer-Encoding: 7bit
Message-ID: <1uydndG6Qf3L75n6nZ2dnZfqnPcAAAAA@giganews.com>
Lines: 34
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-SfRKPnBHcq8PK9lnnS0zbqDKT3xY9qVbwKHbpd3dSj/U/6sgljvNUJbAUgaevSch3Q1qs4kTWSer89w!LBWyAPzKJeNggp/Ous7Xw5bAXdhfqqgLvagoBjxy0D6cMPnnW9R5zJRxnpNrwK9yrA/ysDsgRs/D!yA==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
Bytes: 2678

On 10/07/2024 09:11 AM, Alan Mackenzie wrote:
> FromTheRafters <FTR@nomail.afraid.org> wrote:
>> Alan Mackenzie wrote :
>
> [ .... ]
>
>>> The idea of one countable set being "bigger" than another countable set is
>>> simply nonsense.
>
>> Oops. Finite sets are countable too. :)
>
> Yes indeed!  Thanks for pointing out my mistake.  What I should have
> written (WM please take note) is:
>
> The idea of one countably infinite set being "bigger" than another
> countably infinite set is simply nonsense.
>

Oh, no, there are plenty of "size" relations given other
aspects that merely cardinality that have anything else
to do with what a set models.

For example, there's OUTPACING which makes for that
a proper superset of a set, is larger, by the OUTPACING
relation, it's a fact of mathematics.

And exactly half of the integers are even.
It's called density and it's a property of
them including sets of them.


You're about as bad.