Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 17 Nov 2024 08:50:07 +0100
Organization: A noiseless patient Spider
Lines: 21
Message-ID: <vhc77g$hdd4$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vga7qi$talf$1@dont-email.me>
 <03b90d6c-fff1-411d-9dec-1c5cc7058480@tha.de> <vgb1fj$128tl$1@dont-email.me>
 <vgb2r6$11df6$3@dont-email.me> <vgcs35$1fq8n$1@dont-email.me>
 <vgfepg$22hhn$1@dont-email.me> <vgg0ic$25pcn$1@dont-email.me>
 <vggai3$25spe$8@dont-email.me> <vgi0t7$2ji2i$1@dont-email.me>
 <vgiet5$2l5ni$1@dont-email.me> <vgl2hj$3794c$1@dont-email.me>
 <vgleau$bi0i$2@solani.org> <vgnq3i$3qgfe$1@dont-email.me>
 <vgoka6$3vg2p$1@dont-email.me> <vgq1cm$b5vj$1@dont-email.me>
 <vgq3ca$beif$1@dont-email.me> <vgsp1c$v1ss$1@dont-email.me>
 <vgsq2v$v5t1$1@dont-email.me> <vgvm6h$1k8co$1@dont-email.me>
 <vgvmvr$1kc5f$1@dont-email.me> <vh1vlb$25kic$1@dont-email.me>
 <vh2j89$29gco$1@dont-email.me> <vh4f7p$2o5hn$1@dont-email.me>
 <vh4job$2ov2c$1@dont-email.me> <vh78jp$3cbq7$1@dont-email.me>
 <vh7d5c$3cpaf$1@dont-email.me> <5b8de1bc-9f6c-4dde-a7cd-9e22e8ce19d9@att.net>
 <vhata3$59e5$2@dont-email.me> <31419fde-62b3-46f3-89f6-a48f1fe82bc0@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 17 Nov 2024 08:50:09 +0100 (CET)
Injection-Info: dont-email.me; posting-host="1d28c040c50ba6550151bcf14ba7e1a5";
	logging-data="570788"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+zOb8To5xH5axsKMX/tVic1WV8g3fLY90="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:aImgxnBLhNrR/jCf+dr5YOuIT30=
Content-Language: en-US
In-Reply-To: <31419fde-62b3-46f3-89f6-a48f1fe82bc0@att.net>
Bytes: 2683

On 16.11.2024 23:36, Jim Burns wrote:
> On 11/16/2024 2:54 PM, WM wrote:

>> Therefore
>> the set of intervals cannot grow.
> 
> An infinite set can match a proper superset
> without growing.

But with shrinking. When it matches first itself and then a proper 
subset, then it has decreased. The set of even numbers has fewer 
elements than the set of integers.

> Because it is infinite.

The interval [0, 1] is infinite because it can be split into infinitely 
many subsets. But its measure remains constant. There is no reason 
except naivety to believe that the intervals [n - 1/10,  n + 1/10] could 
cover the real line infinitely often.

Regards, WM