Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!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, 13 Jan 2025 05:51:27 +0100
Organization: A noiseless patient Spider
Lines: 31
Message-ID: <vm264g$1l95f$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>
 <a8b010b748782966268688a38b58fe1a9b4cc087@i2pn2.org>
 <vlei6e$14nve$1@dont-email.me> <66868399-5c4b-4816-9a0c-369aaa824553@att.net>
 <vlir7p$24c51$1@dont-email.me> <417ff6da-86ee-4b3a-b07a-9c6a8eb31368@att.net>
 <vllfof$2n0uj$2@dont-email.me> <07258ab9-eee1-4aae-902a-ba39247d5942@att.net>
 <vlmst2$2vjr0$3@dont-email.me>
 <1ebbc233d6bab7878b69cae3eda48c7bbfd07f88@i2pn2.org>
 <vlo5f4$39hil$2@dont-email.me>
 <4c89380adaad983f24d5d6a75842aaabbd1adced@i2pn2.org>
 <vloule$3eqsr$1@dont-email.me>
 <ffffed23878945243684de7f2aa9aaaf29564508@i2pn2.org>
 <vlrej9$2m5k$1@dont-email.me> <d6ed4797-65e8-4004-853c-f07a37af0c11@att.net>
 <vls4j6$7v2k$3@dont-email.me>
 <adef9ec5c327614374fdc3c3cc55d7a753e28a36@i2pn2.org>
 <vltfo8$heoh$5@dont-email.me>
 <7fc40cc2dbd42016a62aa0374d545e9e787a7da3@i2pn2.org>
 <vltu35$lav6$1@dont-email.me> <vlv88i$sa4k$2@dont-email.me>
 <vm0dl6$15ccj$2@dont-email.me>
 <b27df55b2cd58e362834a1aa0756e860cb5f31c9@i2pn2.org>
 <vm1vsc$1kllp$1@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, 13 Jan 2025 05:51:28 +0100 (CET)
Injection-Info: dont-email.me; posting-host="df5557974a50b0b7a462df9e7dff407a";
	logging-data="1746095"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+ACgTZudN+wR63MOPPLjqY"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:y+idBjDBOMcGB+Mjjzbrlhy0R9M=
In-Reply-To: <vm1vsc$1kllp$1@dont-email.me>
Content-Language: de-DE
Bytes: 2807


>> On 1/12/25 7:47 AM, WM wrote:

>>> All FISONs are less than |ℕ|/n for every n, but their union is |ℕ|.

Mückenheim, Du laberst wieder mal saudummen Schwachsinn daher.

Tatsächlich gilt:

            An e IN: |F(n)| < |IN|
and
            |U_(n e IN) F(n)| = |IN| ,

falls Du das meinst.

Hinweis: Falls (mit n e IN) "|ℕ|/n" jene Kardinalzahl x bezeichnen soll, 
für die x*n = |ℕ| gilt, dann bezeichnet "|ℕ|/n" die Kardinalzahl |ℕ|. Es 
gilt dann also |ℕ|/n = |ℕ|.

Was Du vermutlich meinst/ausdrücken willst, ist, dass für alle k e IN:

            An e IN: |F(k)|*n < |IN|

gilt. D. h. dass jeder Anfangsabschnitt im Vergleich zu IN geradezu 
"verschwindend klein" ist.

..
..
..