Path: news.eternal-september.org!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: The set of necessary FISONs
Date: Tue, 11 Mar 2025 11:00:05 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <81fb12a8d891994f7dff3df3a5f2a86565212c68@i2pn2.org>
References: <vmo1bs$1rnl$1@dont-email.me>
	<8e7b322e-1259-4563-b2d5-37983249a397@att.net>
	<vq7lt1$1uvhg$2@dont-email.me>
	<4ae7b6d4-49a9-47ba-b2ac-c77238e93545@att.net>
	<vq953u$2bkek$1@dont-email.me>
	<b27c5730-4064-4342-aa68-ca4db75fad85@att.net> <vqafli$134ns$1@solani.org>
	<cb1e0570-cdb6-4dab-b5e7-ed37c1cb11dd@att.net> <vqbnrj$14etd$1@solani.org>
	<60614d74-cf15-4e8e-8390-f8861bff44f9@att.net>
	<vqckl7$31ocb$3@dont-email.me>
	<a00f5a07-ba19-4dab-9ab4-fae6f0a64533@att.net>
	<vqedua$3fbs8$1@dont-email.me>
	<e09bc504-743b-42ce-85a7-a815e76f9c26@att.net>
	<vqf5kn$3k3nm$1@dont-email.me>
	<76d99693-1dcf-4049-98b9-a33edced2e83@att.net> <vqh034$2b61$1@dont-email.me>
	<123fb080-4f72-482c-a6e9-aa525aa7150b@att.net> <vqhj2u$62sq$1@dont-email.me>
	<a847e169-4b24-4d5e-9acf-49941173e4e2@att.net> <vqjoi9$ltl6$1@dont-email.me>
	<00fb52fc-ca18-4166-90c7-71b5a66e2dda@att.net> <vqkp9h$sm8g$1@dont-email.me>
	<682d08268062949c28daa5e48fd4823c1b1af4fd@i2pn2.org>
	<vqn00q$1dd7f$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 11 Mar 2025 11:00:05 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="3862814"; 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

Am Mon, 10 Mar 2025 16:20:58 +0100 schrieb WM:
> On 10.03.2025 09:30, joes wrote:
>> Am Sun, 09 Mar 2025 20:13:53 +0100 schrieb WM:
> 
>>> I am interested in the difference that you see between
>>> Z₀ defined by { } ∈ Z₀, and if {{{...{{{ }}}...}}} with n curly
>>> brackets ∈ Z₀ then {{{...{{{ }}}...}}} with n+1 curly brackets ∈ Z₀
>>> and
>>> The set of FISONs failing to have the union ℕ defied by induction:
>>> |ℕ \ {1}| = ℵo, and if |ℕ \ {1, 2, 3, ..., n}| = ℵo then |ℕ \ {1, 2,
>>> 3, ..., n+1}| = ℵo.
>> 
>> How you can view the first set not to have the same union (by Neumann's
>> equivalence) as the the second one would be most welcome. In any case,
>> the second set does not exist according to your contradictory specifi-
>> cation. They are clearly isomorphic.
> 
> That is no my opinion but Jim Burns' opinion.
> Both sets are identical. Both are potentially infinite collections.
No, they are not finite. You can't believe Z_0 to be "complete" in
your sense if you don't think the second set is (and accept that they
are equivalent).

-- 
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.