Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Fri, 14 Feb 2025 14:02:22 +0100
Organization: A noiseless patient Spider
Lines: 49
Message-ID: <vonesu$3f47a$2@dont-email.me>
References: <vmo1bs$1rnl$1@dont-email.me>
 <11e634bd-c1d3-4d72-9e18-be6ca22b4742@att.net> <vo2pit$31hlr$1@dont-email.me>
 <aa038824-04c7-4fde-87f4-b9c3316d30a1@att.net> <vo32p6$3393i$1@dont-email.me>
 <999fb07e-7bef-4423-afeb-a08922613c65@att.net> <vo5cvb$3hukd$1@dont-email.me>
 <be2d9f3e-be38-451a-8598-de19a949cf1e@att.net> <vo7c1q$7ne$3@dont-email.me>
 <0d24c3fd-cd63-4e21-9dd4-ab1360560b09@att.net>
 <cc879e12-d325-48b6-be78-87b8b36cb50d@att.net> <vo8jr7$7mh2$2@dont-email.me>
 <79920977-902d-4f59-a11c-497383221c82@att.net> <voa1r5$ib75$1@dont-email.me>
 <468b9c37-ba93-485c-8685-4b320e168251@att.net> <vocig1$15cth$1@dont-email.me>
 <68bab5c2-50d3-43fc-be0d-51e01c5952bb@att.net> <vof5e4$1n7gr$1@dont-email.me>
 <a52c053a-8537-4f77-849d-aba3cf51283f@att.net> <vog83h$1rvmp$4@dont-email.me>
 <1e5cb0d4-f447-4fa7-b1e9-8056b03d27a2@att.net> <vohp3q$28sjf$1@dont-email.me>
 <fe58cd5f-05ef-41fb-878b-95d30f8beb5f@att.net> <vokn3s$2t0ls$2@dont-email.me>
 <7f762a2f-3d54-4331-a102-cb57b90ffec7@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 14 Feb 2025 14:02:23 +0100 (CET)
Injection-Info: dont-email.me; posting-host="6fd7629c5bdfff525bef709c5ac04246";
	logging-data="3641578"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+DcywtuWWKJv/ad+gsRRVMgz2JDj70tHc="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:GijVJEQaEeDbPYINRoY6upJiBZI=
Content-Language: en-US
In-Reply-To: <7f762a2f-3d54-4331-a102-cb57b90ffec7@att.net>
Bytes: 3170

On 13.02.2025 20:47, Jim Burns wrote:
> On 2/13/2025 7:04 AM, WM wrote:
>> On 13.02.2025 00:49, Jim Burns wrote:
> 
>> Learn that
>> by A(1) and if A(n) then A(n+1)
>> an infinite set is created
> 
> described
> 
>> which has no successors.
> 
> Each FISON has a successor in the set of FISONs.
> The set of FISONs isn't any FISON.

The set of all FISONs is created.
> 
>> Learn that if there were successors,
>> they would have a fixed first element.
> 
> Since induction on the set of FISONs concerns
> a predicate on FISONs, not the set of FISONs,
> presence or absence of successors for
> the set of FISONS and anything else not.in
> the set of FISONs
> is irrelevant.

No, induction concerns alle the natural numbers n of the FISONs A(n).
> 
>> Learn that
>> {1}
>> {2, 1}
>> {3, 2, 1}
>> ...
>> is not longer than broad.
> 
> For each set A which has
> emptier.by.one subsets A\{a} smaller than A
> there is a FISON larger than A

Irrelevant. All are finite and will never become infinite.

> The set of rows and the set of columns
> are both the size of ⋃{F} and each other.
> 
Yes, that is potentially infinite.

Regards, WM