Path: ...!Xl.tags.giganews.com!local-2.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 15 Sep 2024 17:06:10 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Newsgroups: sci.math
References: <vb4rde$22fb4$2@solani.org> <vbnuqq$2it4a$2@dont-email.me>
 <vbp9dk$2u3sh$1@dont-email.me> <vbq4ve$31fu6$10@dont-email.me>
 <fd09e9afa6b0c3041b90c5d788681bb2c92f9d2e@i2pn2.org>
 <vbs9v8$3l368$3@dont-email.me>
 <405557f7289631d63264c712d137244c940b9926@i2pn2.org>
 <vbsroa$3mvi7$2@dont-email.me> <vbt0fs$3pr1d$1@dont-email.me>
 <vbt15n$3qapk$1@dont-email.me> <btbO__HYVIMPfoOcmXp4_whV8-8@jntp>
 <vbums6$8kdn$1@dont-email.me> <vbv9i7$bpjh$2@dont-email.me>
 <13c08e96ad635f8142b38d89863a80caf17a32a8@i2pn2.org>
 <vc1mfe$u3ec$2@dont-email.me>
 <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org>
 <vc1uu8$u3ec$9@dont-email.me> <vc2gfb$130uk$1@dont-email.me>
 <vc44uu$1gc40$1@dont-email.me>
 <c94d6140f000f75c5e95e1acc785ebff9894a18b@i2pn2.org>
 <vc58cf$1o4dp$3@dont-email.me> <87jzfchnxc.fsf@bsb.me.uk>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 15 Sep 2024 10:06:19 -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: <87jzfchnxc.fsf@bsb.me.uk>
Content-Type: text/plain; charset=windows-1252; format=flowed
Content-Transfer-Encoding: 7bit
Message-ID: <kPicnewIWtOfiXr7nZ2dnZfqn_YAAAAA@giganews.com>
Lines: 27
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-L95dsMTDrULAQi4WWinQsgcWjc1lXnU9GYjUX3Y4vQj8Fo2yyK23ZpUrPfAzmhP06YLFfXXptKcmkvG!Vk7Mfrd1qUmhcUE6KcDFmy6XVx5ehN334m70DpoVI9unbELQpN1dar4g60s+NbLE8FjXZqJxlagG
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: 3160

On 09/15/2024 09:38 AM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> On 9/14/2024 11:35 AM, joes wrote:
>>> Am Sat, 14 Sep 2024 16:01:02 +0200 schrieb WM:
>>>> On 14.09.2024 01:05, FromTheRafters wrote:
>>>>> WM explained :
>>>>
>>>>>> No, that is your big mistake. In the interval [0, 1] there is a point
>>>>>> next to 0 and a point next to 1, and infinitely many are beteen them.
>>>>> Define 'next' in this context.
>>>> Two points are next to each other means that no point is between them.
>>> Which is the case for no two (different) reals.
>>
>> Two points on the real line that are different from one another have
>> infinite points between them, and so on and so forth. :^)
>
> It might be worth pointing out that any non-trivial interval [a, b] on
> the real line (i.e. with b > a) contains an uncountable number of
> points.  Constructing the mid point and the quarter points and so on
> only shows a countably infinite number of internal points, but giving a
> bijection between [a, b] and [0, 1] shows that they have the same
> cardinality.
>

Perhaps you might care to define "function" and "topology".