Path: ...!eternal-september.org!feeder3.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
 (extra-ordinary)
Date: Mon, 23 Dec 2024 09:52:42 +0100
Organization: A noiseless patient Spider
Lines: 16
Message-ID: <vkb8cq$14c7u$3@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vjmgdm$i9be$1@dont-email.me>
 <abf7344d-b95b-4432-8626-8356dc1dd261@att.net> <vjn9ud$mlgt$2@dont-email.me>
 <4051acc5-d00a-40d2-8ef7-cf2b91ae75b6@att.net> <vjreik$1lokm$1@dont-email.me>
 <8d69d6cd-76bc-4dc1-894e-709d044e68a1@att.net> <vjst0u$1tqvv$3@dont-email.me>
 <7356267c-491b-45c2-b86a-d40c45dfa40c@att.net> <vjufr6$29khr$3@dont-email.me>
 <4bf8a77e-4b2a-471f-9075-0b063098153f@att.net> <vjv6uv$2dra0$1@dont-email.me>
 <31180d7e-1c2b-4e2b-b8d6-e3e62f05da43@att.net> <vk1brk$2srss$7@dont-email.me>
 <bb80c6c5-04c0-4e2d-bb21-ac51aab9e252@att.net> <vk23m7$31l8v$1@dont-email.me>
 <bce1b27d-170c-4385-8938-36805c983c49@att.net> <vk693m$f52$2@dont-email.me>
 <a17eb8b6-7d11-4c59-b98c-b4d5de8358ca@att.net> <vk7dmb$7mh2$2@dont-email.me>
 <b72490c1-e61a-4c23-a3a5-f624b2c084e4@att.net> <vk8tbq$j9h1$1@dont-email.me>
 <0393b227-fa2e-4649-a363-e53ab6e73327@att.net> <vka3i4$q8gm$1@dont-email.me>
 <vka9gq$rs83$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 23 Dec 2024 09:52:42 +0100 (CET)
Injection-Info: dont-email.me; posting-host="f76a164e5de1a13044de2f0c205d5b55";
	logging-data="1192190"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+F8r0/B2QFQWYIosa/D+bkPzTEFcdcfcc="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:rQ4dRkHaC1w1nZuVl4NKwG+mGjE=
In-Reply-To: <vka9gq$rs83$1@dont-email.me>
Content-Language: en-US
Bytes: 2488

On 23.12.2024 01:05, FromTheRafters wrote:
> WM brought next idea :
>
>> The function E(n) decreases from infinity to zero because in set 
>> theory ℕ \ {1, 2, 3, ...} =  { } is an accepted formula.
> 
> In what way is it decreasing?

One by one. Every endsegment transforms a natural number from content 
inside to index outside. That is guaranteed by mathematics:
∀k ∈ ℕ : ∩{E(0), E(1), E(2), ..., E(k+1)} = ∩{E(0), E(1), E(2), ..., 
E(k)} \ {k+1}. Note the universal quantifier.

Regards, WM