Path: ...!eternal-september.org!feeder2.eternal-september.org!news.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
Date: Thu, 21 Nov 2024 12:27:44 -0800
Organization: A noiseless patient Spider
Lines: 55
Message-ID: <vho53v$podl$1@dont-email.me>
References: <vg7cp8$9jka$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>
 <vhkj2p$25fe$1@dont-email.me> <vhkqs7$4jg8$1@dont-email.me>
 <vhl4lk$5q4u$1@dont-email.me> <vhlfel$8hr6$1@dont-email.me>
 <vhljo1$97jt$1@dont-email.me> <vhlpob$aa52$1@dont-email.me>
 <vhn6a3$jf6v$4@dont-email.me> <vhnb77$la73$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Thu, 21 Nov 2024 21:27:44 +0100 (CET)
Injection-Info: dont-email.me; posting-host="d9e58977d2d48dce1140db71cc33613f";
	logging-data="844213"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+wvTRGw1Hkl5EC3qeFicuE1bA7VnMUjY8="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:sCMJtiZNNWSv48Qe28hYEa5hnjk=
In-Reply-To: <vhnb77$la73$1@dont-email.me>
Content-Language: en-US
Bytes: 4104

On 11/21/2024 5:05 AM, FromTheRafters wrote:
> WM wrote :
>> On 21.11.2024 00:01, FromTheRafters wrote:
>>> After serious thinking WM wrote :
>>>> On 20.11.2024 21:05, FromTheRafters wrote:
>>>>> WM wrote on 11/20/2024 :
>>>>>> On 20.11.2024 15:14, FromTheRafters wrote:
>>>>>>> WM formulated on Wednesday :
>>>>>>
>>>>>>>>
>>>>>>>> It does not make it wrong, but it unmasks it at imprecise. 
>>>>>>>> That's why I don't like it. We can do better.
>>>>>>>
>>>>>>> It works well enough.
>>>>>>
>>>>>> Really? Then you can answer the following questions:
>>>>>>
>>>>>> Let every unit interval after a natural number on the real axis be 
>>>>>> coloured white with exception of the powers of 2 which are 
>>>>>> coloured black. Is it possible to shift the black intervals so 
>>>>>> that the whole real axis becomes black?
>>>>>
>>>>> No, of course not.
>>>>
>>>> Thank you. You are the first person not bewitched by set theory.
>>>
>>> The real line is infinitely long in both directions. Your shifted 
>>> intervals are all on the positive real axis.
>>
>> But if Cantor was right, all integers, positive as well as all other 
>> could be in bijection with the powers of 2.
> 
> Integer powers of two? Yes, both are countable sets.
> 
>>>>> Depending on the order of the tasks. I think half red or half black.
>>>>
>>>> Recidivistic?
>>>
>>> I recognize McDuck in disguise, or your notion that there are fewer 
>>> primes than there are natural numbers. You keep finding different 
>>> ways to say the same wrong thing.
>>
>> The analytical limit is wrong in your opinion?
> 
> Which limit? Is a half-plane smaller than a whole plane? Is a ray 
> shorter than a line? Is a line segment shorter than a ray? What size 
> symbol could you write on a whole plane that you could not write on a 
> half plane? If McDuck's earnings always outpace his spending how can one 
> consider him ever going bankrupt 'in the limit'? Which limit?

Gotta love half-plane to disc conformal mapping...

https://www.facebook.com/photo/?fbid=297639734728365&set=a.110008616824812

;^)