Path: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 19 Jan 2025 15:02:22 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <4c768985a7a52263bf11b3bc363d4d55ade3e1d5@i2pn2.org>
References: <vg7cp8$9jka$1@dont-email.me> <vlrej9$2m5k$1@dont-email.me>
	<d6ed4797-65e8-4004-853c-f07a37af0c11@att.net> <vls4j6$7v2k$3@dont-email.me>
	<494bfd3b-3c70-4d8d-9c70-ce917c15fc22@att.net>
	<vm0okb$16cq0$2@dont-email.me>
	<bff18686-503a-4b7b-9406-b47796f68b47@att.net>
	<vm15pj$18v7t$1@dont-email.me>
	<72142d82-0d71-460a-a1be-cadadf78c048@att.net>
	<vm3hrs$1s9ld$2@dont-email.me>
	<812e64b1-c85c-48ac-a58c-e8955bc02f8c@att.net>
	<vm59g4$2b5ib$1@dont-email.me>
	<22b74adc-bf38-4aa4-a44f-622f0a2a5c41@att.net>
	<vm8u36$31v8s$5@dont-email.me>
	<77a1069f5c5b8f95927ed9a33ecc6374c9d0a2dd@i2pn2.org>
	<vmb821$3i6nm$1@dont-email.me>
	<da8e83072697acf06f9ca2b2946d7b9ccfcbcaac@i2pn2.org>
	<20e517f6-d709-46fd-83f8-04c6b4fe9f59@tha.de>
	<4679319ea238a03fb042ae0c4de078c1a310c8a5@i2pn2.org>
	<vmejlt$845r$1@dont-email.me>
	<320edbb95673eb535f81c16a471811fef7d0f752@i2pn2.org>
	<vmijvi$24teu$1@dont-email.me> <vmikvk$25bmm$1@dont-email.me>
	<vmilv3$24teu$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 19 Jan 2025 15:02:22 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="148837"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM";
User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a
 git.gnome.org/pan2)
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 3348
Lines: 35

Am Sun, 19 Jan 2025 11:59:47 +0100 schrieb WM:
> On 19.01.2025 11:42, FromTheRafters wrote:
>> WM presented the following explanation :
>>> On 18.01.2025 12:03, joes wrote:
>>>> Am Fri, 17 Jan 2025 22:56:13 +0100 schrieb WM:
>>>
>>>>> Correct. If infinity is potential. set theory is wrong.
>>>> And that is why set theory doesn't talk about "potential infinity".
>>> Nevertheless it uses potential infinity.
>> No, it doesn't.
> Use all natnumbers individually such that none remains. Fail.
Set theory doesn't use "potential infinity".

>>> All "bijections" yield the same cardinality because only the
>>> potentially infinite parts of the sets are  applied.
Quite the opposite.
>> No, it is because these bijections show that some infinite sets' sizes
>> can be shown to be equal even if no completed count exists.
> They appear equal because no completed count exists.
The "complete count" is infinite.

> All natnumbers in bijections have ℵ₀ not applied successors.
A bijection is not meant to be thought about sequentially?

> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo Only potential infinity is
> applied.
This is not infinity.

> In actual infinity all natnumbers would be applied:
> ℕ \ {1, 2, 3, ...} = { }
> But that is not possible in bijections.
It absolutely is. Just give a rule for every natural.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.