Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sat, 14 Dec 2024 09:08:48 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <e20e2d1502c1fdc0c370c7bd61f767f1ec932446@i2pn2.org>
References: <vg7cp8$9jka$1@dont-email.me> <vgi0t7$2ji2i$1@dont-email.me>
 <vgiet5$2l5ni$1@dont-email.me> <vgl2hj$3794c$1@dont-email.me>
 <vgleau$bi0i$2@solani.org> <vgnq3i$3qgfe$1@dont-email.me>
 <vgoka6$3vg2p$1@dont-email.me> <vgq1cm$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> <vh9o5u$3un1v$1@dont-email.me>
 <vhasiv$59e5$1@dont-email.me> <vhcb2r$i5se$1@dont-email.me>
 <vhcgic$hge9$1@dont-email.me> <vhcngu$kmv2$1@dont-email.me>
 <35274130-ffa0-4d11-b634-f2feb3851416@tha.de> <vhf33f$16f4o$1@dont-email.me>
 <f7fab959-0408-49c1-8e1c-d93e389e3021@tha.de> <vhhlvf$1p6v4$1@dont-email.me>
 <vhhrb7$1q0r9$2@dont-email.me> <vjjgbq$3u217$1@dont-email.me>
 <vjjh1u$3tvsg$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 14 Dec 2024 14:08:49 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="2822012"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
X-Spam-Checker-Version: SpamAssassin 4.0.0
Content-Language: en-US
In-Reply-To: <vjjh1u$3tvsg$3@dont-email.me>
Bytes: 3778
Lines: 47

On 12/14/24 3:53 AM, WM wrote:
> On 14.12.2024 09:41, Mikko wrote:
>> On 2024-11-19 11:04:08 +0000, WM said:
>>
>>> On 19.11.2024 10:32, Mikko wrote:
>>>> On 2024-11-18 14:29:40 +0000, WM said:
>>>>
>>>>> On 18.11.2024 10:58, Mikko wrote:
>>>>>> On 2024-11-17 12:46:29 +0000, WM said:
>>>>>
>>>>>>> There are 100 intervals for each natural number.
>>>>>>> This can be proven by bijecting J'(100n) and J(n). My intervals 
>>>>>>> are then exhausted, yours are not.
>>>>>>
>>>>>> Irrelevant.
>>>>>
>>>>> Very relevant.
>>>>
>>>> It is not relevant if no relevancy is shown.
>>>
>>> But if relevancy is only deleted, it can show up again:
>>>
>>> Every finite translation of any finite subset of intervals J(n) 
>>> maintains the relative covering 1/5. If the infinite set has the 
>>> relative covering 1 (or more), then you claim that the sequence 1/5, 
>>> 1/5, 1/5, ... has limit 1 (or more).
>>
>> There is a bijection between your J and my J', where
>> J'(n) = (n/100 - 1/10, n/100 + 1/10): for each n there
>> is one interval J(n) and one interval of J'(n). Whateever
>> you infer from that is either an invalid inference or
>> a true conclusion.
>>
> Please refer to the simplest example I gave you on 2024-11-27:
> The possibility of a bijection between the sets ℕ = {1, 2, 3, ...} and D 
> = {10n | n ∈ ℕ} is contradicted because for every interval (0, n] the 
> relative covering is not more than 1/10, and there are no further 
> numbers 10n beyond all natural numbers n. The sequence 1/10, 1/10, 
> 1/10, ... has limit 1/10.
> 
> Regards, WM
> 

Except that we aren't dealng with the FINITE sets of {1, 2, 3, ..., n} 
but for the full set of { 1, 2, 3, ... }

All you are proving is that you don't understand that infinity isn't 
finite, and that you logic is basdd on LIES.