Path: ...!eternal-september.org!feeder3.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
 (extra-ordinary)
Date: Mon, 16 Dec 2024 09:30:18 +0100
Organization: A noiseless patient Spider
Lines: 35
Message-ID: <vjooeq$11n0g$2@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vi6p1l$3uoti$1@dont-email.me>
 <vi6unr$3v0dn$5@dont-email.me> <vihd3l$2d9fk$1@dont-email.me>
 <vihfai$2cnof$1@dont-email.me> <vijrru$37ce1$1@dont-email.me>
 <vikh9k$3cua3$1@dont-email.me> <viml28$6j3$1@dont-email.me>
 <0b1bb1a1-40e3-464f-9e3d-a5ac22dfdc6f@tha.de>
 <95183b4d9c2e32651963bac79965313ad2bfe7e8@i2pn2.org>
 <vj6vhh$elqh$2@dont-email.me>
 <33512b63716ac263c16b7d64cd1d77578c8aea9d@i2pn2.org>
 <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>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 16 Dec 2024 09:30:19 +0100 (CET)
Injection-Info: dont-email.me; posting-host="8cb16b437f3efafb0eb1892e9ae812c7";
	logging-data="1104912"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+sL+IEYP8MhwRia5Y1A7736ofv0Te1SoE="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:CnMHqUryFRCVNlGcLFs4xDik/vM=
In-Reply-To: <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org>
Content-Language: en-US
Bytes: 3483

On 15.12.2024 21:21, joes wrote:
> Am Sun, 15 Dec 2024 16:25:55 +0100 schrieb WM:
>> On 15.12.2024 12:15, joes wrote:
>>> Am Sat, 14 Dec 2024 17:00:43 +0100 schrieb WM:
>>
>>>>>>>> That pairs the elements of D with the elements of ℕ. Alas, it can
>>>>>>>> be proved that for every interval [1, n] the deficit of hats
>>>>>>>> amounts to at least 90 %. And beyond all n, there are no further
>>>>>>>> hats.
>>>>>>> But we aren't dealing with intervals of [1, n] but of the full set.
>>>>>> Those who try to forbid the detailed analysis are dishonest
>>>>>> swindlers and tricksters and not worth to participate in scientific
>>>>>> discussion.
>>>>> No, we are not forbiding "detailed" analysis
>>>> Then deal with all infinitely many intervals [1, n].
>>> ??? The bijection is not finite.
>> Therefore we use all [1, n].
> Those are all finite.

All n are finite.
> 
>>>>>>> The problem is that you can't GET to "beyond all n" in the pairing,
>>>>>>> as there are always more n to get to.
>>>>>> If this is impossible, then also Cantor cannot use all n.
>>>>> Why can't he? The problem is in the space of the full set, not the
>>>>> finite sub sets.
>>>> The intervals [1, n] cover the full set.
>>> Only in the limit.
>> With and without limit.
> Wonrg. There is no natural n that „covers N”.

All intervals do it because there is no n outside of all intervals [1, 
n]. My proof applies all intervals.

Regards, WM