Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Wed, 20 Nov 2024 13:01:29 +0100
Organization: A noiseless patient Spider
Lines: 20
Message-ID: <vhkj2p$25fe$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>
 <cb0c9917-09a9-45f0-8fe9-cd059fa82dde@att.net> <vh4itg$2o3vu$1@dont-email.me>
 <8165b44b-1ba5-429d-8317-0b043b214b53@att.net> <vh76bi$3bnde$1@dont-email.me>
 <d90452a5-965b-443f-9146-96cdf9b3906c@att.net> <vh8ft0$3jqb5$3@dont-email.me>
 <vh8g5e$3juug$1@dont-email.me> <vh8otd$3lhlt$2@dont-email.me>
 <vhb1is$6hbv$2@dont-email.me> <vhb1mu$6hbv$4@dont-email.me>
 <vhb32t$7ese$1@dont-email.me> <vhch7n$hge9$2@dont-email.me>
 <vhcieh$jjk5$1@dont-email.me> <vhcjg5$hdd4$3@dont-email.me>
 <vhckkh$k32g$1@dont-email.me> <vhcp0r$hge9$6@dont-email.me>
 <vhd7d7$nt37$1@dont-email.me> <vhd9lq$obb0$1@dont-email.me>
 <883377b7ebbd9d5d528db048daf9f682e3854ae8@i2pn2.org>
 <vhdfu1$p3fg$2@dont-email.me> <vhdlgc$qod3$1@dont-email.me>
 <vhfrnd$1adlc$2@dont-email.me> <vhfsfu$1bgpj$1@dont-email.me>
 <vhfuta$1adlc$3@dont-email.me> <vhgd02$1ep1p$1@dont-email.me>
 <vhge3n$1eu67$1@dont-email.me> <vhgfec$1f6mn$1@dont-email.me>
 <vhi8c0$1sjsn$1@dont-email.me> <vhif1d$1u4gp$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Wed, 20 Nov 2024 13:01:30 +0100 (CET)
Injection-Info: dont-email.me; posting-host="10af3bc7caee4ceaa4972e93614969c0";
	logging-data="71150"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18f8IDnJoDb3s+KcDDHFdAuWb34M6C4DBU="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:fiKXQlxcYXv6kGr1n/IKCXjgDVg=
In-Reply-To: <vhif1d$1u4gp$1@dont-email.me>
Content-Language: en-US
Bytes: 2594

On 19.11.2024 17:40, FromTheRafters wrote:
> WM was thinking very hard :

>> Only finite sets are countable.
> 
> Wrong, it is countable if there is a bijection.

They are erroneously called countable, but they are not countable.

>> But all "countably" infinite sets have the same size, which according 
>> to the different numbers of elements is a very unsharp measure.
> 
> That you don't like cardinal arithmetic, doesn't make cardinal 
> arithmetic wrong.

It does not make it wrong, but it unmasks it at imprecise. That's why I 
don't like it. We can do better.

Regards, WM