Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 1 Feb 2025 19:33:54 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <bf10f777d4005fb3ee28e246cbe0245d554223d3@i2pn2.org>
References: <vmo1bs$1rnl$1@dont-email.me>
 <d90c478d-6806-4ffe-83be-a5d7674bb5e3@att.net>
 <b82a0915-400a-4f77-9309-44eef432e9f4@att.net> <vn50eo$3kgi6$2@dont-email.me>
 <4d349964-211f-42f1-936f-81c22ae54cb5@att.net> <vn7vns$ra97$2@dont-email.me>
 <e3f89d8c-d214-453a-91f4-9023e744fed2@att.net> <vna72s$1ng1k$2@dont-email.me>
 <6e0c8ab2-402a-43a5-a348-0c727eae6a2e@att.net> <vnat4s$1s6ha$4@dont-email.me>
 <e43b1c65-4424-4e0c-9b2e-65e0e463815b@att.net> <vnconr$29v5v$1@dont-email.me>
 <87e2e677c7802c9c17df6063f340cb5857d5700b@i2pn2.org>
 <vnd4h8$2c0st$1@dont-email.me>
 <c50fde56e7e0c4cf4842d4944ea3d1917c75eb41@i2pn2.org>
 <vnfftp$2rv3t$1@dont-email.me>
 <680d4249c9bf1504231a53732ac5096184261495@i2pn2.org>
 <vngk12$31ud4$5@dont-email.me>
 <5cc37d5ccc25d192843fcaf87e7418be0e9c5136@i2pn2.org>
 <vni8b7$3f2gg$3@dont-email.me>
 <b3661d4e001c1467c1121af3f013304666ac40bf@i2pn2.org>
 <vnl5dv$3ae6$2@dont-email.me>
 <080c854de10093669d87615694e51dd052ed2394@i2pn2.org>
 <vnlog6$6dbv$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 2 Feb 2025 00:33:54 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="2256190"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
In-Reply-To: <vnlog6$6dbv$2@dont-email.me>
X-Spam-Checker-Version: SpamAssassin 4.0.0
Content-Language: en-US
Bytes: 2711
Lines: 23

On 2/1/25 1:17 PM, WM wrote:
> On 01.02.2025 15:09, joes wrote:
> 
>> The set of necessary FISONs has no first element, being empty.
>>
> The set of FISONs assumed to satisfy U(A(n)) = ℕ cannot be empty. But we 
> can prove by induction that every FISON can be discarded without 
> changing the union. That disproves the assumption.
> 
> Regards, WM

And that is your problem, you make assumptions that are unwarented, and 
then blaim reality for not matching your assumptions.

YOU are the one that is wrong.

Or, do you think that 36 can't be factored, since no one factor of 36 is 
required to factor it?

(You have agreed to that statement by not showing how you logic doesn't 
say that).

We can form MANY set of FISONs whose union will be the set of Natural 
Numbers, so you claim is just a falsehood.