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: Thu, 21 Nov 2024 22:57:52 +0100
Organization: A noiseless patient Spider
Lines: 34
Message-ID: <vhoad2$qkpu$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vgq1cm$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$2@dont-email.me> <31419fde-62b3-46f3-89f6-a48f1fe82bc0@att.net>
 <vhc77g$hdd4$1@dont-email.me> <476ae6cb-1116-44b1-843e-4be90d594372@att.net>
 <vhhr6f$1q0r9$1@dont-email.me> <ffa63cb5-8898-4aa7-80eb-8b2c51c9986d@att.net>
 <vhkhun$28qt$1@dont-email.me> <vhmtph$j1ek$1@dont-email.me>
 <vhn1jk$jf6v$1@dont-email.me> <27b8de9e-a17e-4116-ab5e-1e552bea0fce@att.net>
 <vhnmsi$n2pc$1@dont-email.me> <6d0d8060-fb60-4da6-bcdb-adc13a6179b0@att.net>
 <vho171$otvf$1@dont-email.me> <93c53518-55f8-4dca-aa3c-3e79ef268963@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Thu, 21 Nov 2024 22:57:55 +0100 (CET)
Injection-Info: dont-email.me; posting-host="b99cd19fe595d2e368def072eb90a4c2";
	logging-data="873278"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/RD7FxqM8hqU77Cbq5Th1idIi80/shiTs="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:M7kzePZPR5Mqed0ZbEgiaWSZaaw=
In-Reply-To: <93c53518-55f8-4dca-aa3c-3e79ef268963@att.net>
Content-Language: en-US
Bytes: 2979

On 21.11.2024 22:46, Jim Burns wrote:
> On 11/21/2024 2:21 PM, WM wrote:
>> On 21.11.2024 19:54, Jim Burns wrote:
>>> On 11/21/2024 11:24 AM, WM wrote:
> 
>>>> By what is it covered,
>>>> after all n have been proved unable?
>>>
>>> ⎛ n ↦ i/j ↦ n
>>> ⎜
>>> ⎜ (i+j) := ⌈(2⋅n+¼)¹ᐟ²+½⌉
>>> ⎜ i := n-((i+j)-1)⋅((i+j)-2)/2
>>> ⎜ j := (i+j)-i
>>> ⎜
>>> ⎝ (i+j-1)⋅(i+j-2)/2+i = n
>>
>> That is not an answer.
> 
> You (WM) see it as "indistinguishable from magic".
> That's a shame for your students.

To believe that the intervals can colour the real axis black is a shame 
for all members of humankind who do so.

> The _description_ is completed.
> It's right there.

The description of the set not of all its elements.

Either limits can be calculated from the finite, or not. If not, then 
Cantor's attempts are in vain from the scratch. If yes, then Cantor's 
attempts have been contradicted.

Regards, WM