Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 2 Dec 2024 09:00:30 +0100
Organization: A noiseless patient Spider
Lines: 32
Message-ID: <vijpeu$36aql$4@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>
 <67d9867b-2614-4475-975c-938bafca5c00@att.net> <vi1vep$2pjuo$1@dont-email.me>
 <a4ab640d-e482-42b0-bfb8-f3690b935ce1@att.net> <vi41rg$3cj8q$1@dont-email.me>
 <d124760c-9ff9-479f-b687-482c108adf68@att.net> <vi56or$3j04f$1@dont-email.me>
 <4a810760-86a1-44bb-a191-28f70e0b361b@att.net> <vi6uc3$3v0dn$4@dont-email.me>
 <b2d7ee1f-33ab-44b6-ac90-558ac2f768a7@att.net> <vi7tnf$4oqa$1@dont-email.me>
 <23311c1a-1487-4ee4-a822-cd965bd024a0@att.net>
 <e9eb6455-ed0e-43f6-9a53-61aa3757d22d@tha.de>
 <71758f338eb239b7419418f49dfd8177c59d778b@i2pn2.org>
 <via83s$jk72$2@dont-email.me> <viag8h$lvep$1@dont-email.me>
 <viaj9q$l91n$1@dont-email.me> <vibvfo$10t7o$1@dont-email.me>
 <vic6m9$11mrq$4@dont-email.me> <vicbp2$1316h$1@dont-email.me>
 <vid4ts$1777k$2@dont-email.me> <vidcv3$18pdu$1@dont-email.me>
 <bdbc0e3d-1db2-4d6a-9f71-368d36d96b40@tha.de> <vier32$1madr$1@dont-email.me>
 <vierv5$1l1ot$2@dont-email.me> <viiqfd$2qq41$5@dont-email.me>
 <vijob7$36aql$2@dont-email.me>
Reply-To: invalid@example.invalid
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 02 Dec 2024 09:00:31 +0100 (CET)
Injection-Info: dont-email.me; posting-host="42f5c2b502c9af350f9bc6411f7fd1ea";
	logging-data="3353429"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX182Lzh6rOCDx0hdzvT0TqSS"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:8BwqYuCrd/b4cowEoC90NMQcOeE=
Content-Language: de-DE
In-Reply-To: <vijob7$36aql$2@dont-email.me>
Bytes: 3091

Am 02.12.2024 um 08:41 schrieb Moebius:
> Am 02.12.2024 um 00:11 schrieb Chris M. Thomasson:
>> On 11/30/2024 3:12 AM, WM wrote:
> 
> FISON(s)
> 
>>> Finite initial segment[s]: F(n) = {1, 2, 3, ..., n}   (n e IN)
> 
> You see it's a DEFINITION:
> 
>          F(n) = {1, 2, 3, ..., n}   (n e IN) .

 From this definition we may get an explicit definition for the term 
/FISON/ (short for "finite initial segment"):

            X is a /FISON/ iff there is an n e IN such that X = F(n).

> This "means" (implies): F(1) (i.e. {1}) is a FISON, F(2) (i.e. {1, 2}) is a FISON, 
> F(3) (i.e. {1, 2, 3}) is a FISION, and so on (ad infinitum). F(1), F(2), F(3), ... are FISONs.
> 
>> Finite? 
> 
> Yeah, finite. For each and eveer n e IN F(n) (i.e. {1, 2, 3, ..., n}) is 
> finite (i.e. a finite set).
> 
> Huh? The natural numbers don't stop at n! WTF!!!
> 
> No one (except possibly Mückenheim) said they did.
> 
> Hint: There are _infinitely many_ finite initial segments (one for each 
> and every natural number n). :-)