Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 29 Dec 2024 14:15:32 -0800
Organization: A noiseless patient Spider
Lines: 35
Message-ID: <vkshm4$17741$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vj9s4i$11a3p$1@dont-email.me>
 <vjam6d$1700v$1@dont-email.me> <vjc65g$1i9vk$3@dont-email.me>
 <vjf7kl$2s7e5$1@dont-email.me> <vjfmq3$2upa9$3@dont-email.me>
 <c6b624cb0b1b55d54aab969ee5b4e283ec7be3cd@i2pn2.org>
 <vjhp8b$3gjbv$1@dont-email.me>
 <dc9e7638be92c4d158f238f8c042c8559cd46521@i2pn2.org>
 <vjjg6p$3tvsg$1@dont-email.me>
 <c31edc62508876748c8cf69f93ab80c0a7fd84ac@i2pn2.org>
 <vjka3b$1tms$3@dont-email.me>
 <e11a34c507a23732d83e3d0fcde7b609cdaf3ade@i2pn2.org>
 <vjmse3$k2go$2@dont-email.me>
 <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org>
 <vjooeq$11n0g$2@dont-email.me>
 <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org>
 <vjrfcc$1m1b2$1@dont-email.me>
 <75921cc1f17cdb691969a99e666f237cd09c0b09@i2pn2.org>
 <vjsrp1$1tqvv$2@dont-email.me>
 <25729298b142c60d5b245231984119d42d4ac089@i2pn2.org>
 <vko14j$53b6$3@dont-email.me> <vko1vp$5mmo$1@dont-email.me>
 <vko2a3$5mmo$3@dont-email.me> <vkpkbr$fnhj$2@dont-email.me>
 <vkraki$tpqs$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 29 Dec 2024 23:15:33 +0100 (CET)
Injection-Info: dont-email.me; posting-host="ed7476352251308ea5932b030c92726f";
	logging-data="1285249"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18/dLhRZzKSL5WxF8Z2CkZLlS9JMcZMRwI="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:WFGj/scgJqdI2hH4y/LleFFJaL0=
Content-Language: en-US
In-Reply-To: <vkraki$tpqs$3@dont-email.me>
Bytes: 2783

On 12/29/2024 3:09 AM, WM wrote:
> On 28.12.2024 20:42, Moebius wrote:
> 
>>> Hint: For each and every n e IN there is a singleton such that n is 
>>> in it (namely {n}).
>>>
>>> BUT there's no singleton such that each and every n e IN is in it.
> 
> My theorem: Every union of FISONs which stay below a certain threshold 
> stays below that threshold.

The threshold is finite.

{ 1 }, { 1, 2 }, { 1, 2, 3 }, ...

threshold = 3

{ 1 }, { 1, 2 }, { 1, 2 (3) }, three is invalid so:

{ 1 }, { 1, 2 }

// combining things and removing duplicates

{ 1, 2 }

This is finite thinking.



> 
> Find a counterexample. Don't claim it but prove it. Fail.
> 
> Regards, WM
>