Warning: mysqli::__construct(): (HY000/1203): User howardkn already has more than 'max_user_connections' active connections in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\includes\artfuncs.php on line 21
Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connections
Warning: mysqli::query(): Couldn't fetch mysqli in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\index.php on line 66
Article <vf085m$1gf6$1@news.muc.de>
Deutsch   English   Français   Italiano  
<vf085m$1gf6$1@news.muc.de>

View for Bookmarking (what is this?)
Look up another Usenet article 
Path: ...!3.eu.feeder.erje.net!feeder.erje.net!news.szaf.org!news.karotte.org!news.space.net!news.muc.de!.POSTED.news.muc.de!not-for-mail
From: Alan Mackenzie <acm@muc.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sat, 19 Oct 2024 12:20:06 -0000 (UTC)
Organization: muc.de e.V.
Message-ID: <vf085m$1gf6$1@news.muc.de>
References: <vb4rde$22fb4$2@solani.org>   <vejte9$e3ds$1@solani.org> <53460f91-4542-4a92-bc4b-833c2ad61e52@att.net> <ventec$255vi$2@dont-email.me> <venunr$2533b$4@dont-email.me> <29ce40e9-f18a-44d4-84d9-23e587cf9dea@att.net> <veor6u$2asus$1@dont-email.me> <2b6f9104-a927-49ee-9cf0-6ee3f82edc23@att.net> <verkkk$2r6kk$1@dont-email.me> <verlk6$4dv$1@news.muc.de> <vermdv$2s24h$1@dont-email.me> <verv6f$2oo0$1@news.muc.de> <e4d00f83-42df-4f14-a007-4a90f3b5d644@tha.de>
Injection-Date: Sat, 19 Oct 2024 12:20:06 -0000 (UTC)
Injection-Info: news.muc.de; posting-host="news.muc.de:2001:608:1000::2";
	logging-data="49638"; mail-complaints-to="news-admin@muc.de"
User-Agent: tin/2.6.3-20231224 ("Banff") (FreeBSD/14.1-RELEASE-p3 (amd64))
Bytes: 2429
Lines: 33

WM <wolfgang.mueckenheim@tha.de> wrote:
> On 17.10.2024 23:22, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:

>>> If you can't understand or don't believe, then there is no common basis
>>> for discussion.

>> It's not a matter of belief.  It's a matter of correct and rigorous
>> mathematics.

> When doubling natural numbers we obtain even numbers which have not been 
> doubled.

> This is a sentence that every mathematician can understand.

It is not - it is ill formed and ambiguous.  It doesn't say which
natural numbers are being doubled.  It is unmathematical in that it
seems to posit a doubling being done one element at a time, rather than
the standard mathematical concept of a mapping from N -> N where n is
mapped to 2n.  In this standard notion, all numbers are doubled, and we
encounter no undoubled even natural numbers.

> It is true because the interval covered by the doubled numbers is
> twice as large as the interval covered by the numbers to be doubled.

The interval is infinite.  "Doubling" an infinite set yields a set of
the same size as the original - there is a 1-1 correspondence between
them.

> Regards, WM

-- 
Alan Mackenzie (Nuremberg, Germany).