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, 13 Nov 2024 22:29:18 +0100
Organization: A noiseless patient Spider
Lines: 71
Message-ID: <vh35nd$2d81g$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vgg57o$25ovs$2@dont-email.me>
 <71fea361-0069-4a98-89a4-6de2eef62c5e@att.net> <vggh9v$27rg8$3@dont-email.me>
 <ff2c4d7c-33b4-4aad-a6b2-88799097b86b@att.net> <vghuoc$2j3sg$1@dont-email.me>
 <d79e791d-d670-4a5a-bd26-fdf72bcde6bc@att.net> <vgj4lk$2ova9$3@dont-email.me>
 <f154138e-4482-4267-9332-151e2fd9f1ba@att.net> <vgkoi7$b5pp$1@solani.org>
 <6d9f3b10-47ad-459c-9536-098ce91f514b@att.net> <vgni02$3osmc$1@dont-email.me>
 <16028da0-456b-47ad-8baa-7982a7cbdf10@att.net> <vgpupb$abrr$2@dont-email.me>
 <fc4df00f-96d1-402f-89d2-739cb8ddd863@att.net> <vgsg04$t7fk$1@dont-email.me>
 <1fca3a53-1cb4-4fd2-85b6-85e9b69ca23b@att.net> <vgtpmo$153hf$6@dont-email.me>
 <d17f7542-986e-4897-89b4-dccaf11d5311@att.net> <vh00jj$1m6co$1@dont-email.me>
 <97304048-24f5-4625-82a7-d17427f2f6e3@att.net> <vh0hta$1pmql$1@dont-email.me>
 <65febd06-662b-4fa4-9aa8-f7353a79a110@att.net> <vh2k9p$29cql$1@dont-email.me>
 <157a949d-6c19-4693-8cee-9e067268ae45@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 13 Nov 2024 22:29:18 +0100 (CET)
Injection-Info: dont-email.me; posting-host="faf4652390a146df235861e855eb1b63";
	logging-data="2531376"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+IAe/ehuig6qBpBMMjWKbjs+td68uEQZw="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:uZeAIuetT+CDnC/gEHnz9B5EUNc=
In-Reply-To: <157a949d-6c19-4693-8cee-9e067268ae45@att.net>
Content-Language: en-US
Bytes: 3738

On 13.11.2024 20:38, Jim Burns wrote:
> On 11/13/2024 11:31 AM, WM wrote:

>>
>> If infinite sets obey the rules sketched above,
> 
> ... _and are finite_ ...

Not necessary to apply logic, geometry and analysis.
> 
>> then set theorists must discard geometry
>> because
>>  by shifting intervals
>>  the relative covering 1/5 of ℝ+ becomes oo*ℝ,
>> and analysis
>> because
>>  the constant sequence 1/5, 1/5, 1/5, ...
>>  has limit oo,
>> and logic
>> because of
>>  Bob.
> 
> ----
>>  by shifting intervals
>>  the relative covering 1/5 of ℝ+ becomes oo*ℝ,
> 
> By definition,
> the value of a measure is an extended real≥0

The value of the relative measure is 1/5. For every finite interval this 
is true. The limit can be calculated in analysis of real numbers without 
extension.
> 
> An extended real≥0 is either
> Archimedean == having a countable.to bound,  or
> non.Archimedean == not.having a countable.to bound.
> 
> The extended reals≥0 have only
> the standard reals≥0, which are Archimedean, and
> a single non.Archimedean point≥0  +∞

That is what I call ω. But the limit can be calculated from the reals 
alone, in particular when the sequence is constant.
> 
> No,
> the measure doesn't _become_ +∞
> It has the same value +∞ before and after shifting.

Take the relative measure that can be obtained from every finite 
interval of the real line.
> 
> ----
>>  the constant sequence 1/5, 1/5, 1/5, ...
>>  has limit oo,
> 
Nonsense deleted.
> 
> ----
>>  Bob.
> 
> KING BOB!
> https://www.youtube.com/watch?v=TjAg-8qqR3g
> 
> If,
>   in a set A which
>   can match one of its proper subsets B,
>
That is nonsense too.

Regards, WM