Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!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: Sun, 16 Feb 2025 18:16:44 +0100
Organization: A noiseless patient Spider
Lines: 15
Message-ID: <vot6hr$lfa0$3@dont-email.me>
References: <vmo1bs$1rnl$1@dont-email.me>
 <79920977-902d-4f59-a11c-497383221c82@att.net> <voa1r5$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>
 <b9b0c514-a71c-4cd8-b291-a4847db04795@att.net> <vokmsi$2t0ls$1@dont-email.me>
 <8a4c44c4ba0d3260a90d463acfa814fbc83f557a@i2pn2.org>
 <voktdg$2tt35$1@dont-email.me>
 <853f9685ed5be27fedb6486ca2931ef189b920df@i2pn2.org>
 <vonjm5$3ghe5$1@dont-email.me>
 <5aefc0d0b454a230e721a8cdb8400cb25ea9a8c1@i2pn2.org>
 <vonqus$3hu2d$1@dont-email.me>
 <f220383b9803059a387c34e198906c7729101311@i2pn2.org>
 <vopv2h$s46$2@dont-email.me>
 <340761ab1ceb68741d949331a0c64a3d6d5fa237@i2pn2.org>
 <vosf9f$hjfh$4@dont-email.me>
 <e65f39b64ea4a5bb0fd1b8d214fbf99c4a5a0b23@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 16 Feb 2025 18:16:43 +0100 (CET)
Injection-Info: dont-email.me; posting-host="ed230be1e1a3971a391d4c6488812bee";
	logging-data="703808"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/WfAA2S9AqyW7uX6tfFQbz48IPrijTAX4="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:p+hgFaki24aSsuFvxjypCoVqAss=
Content-Language: en-US
In-Reply-To: <e65f39b64ea4a5bb0fd1b8d214fbf99c4a5a0b23@i2pn2.org>
Bytes: 2528

On 16.02.2025 13:34, Richard Damon wrote:
> On 2/16/25 5:39 AM, WM wrote:
>> On 15.02.2025 18:54, joes wrote:
>>> No element of the set of FISONs is
>>> necessary
>>
>> Therefore all can be removed, and U(F) = ℕ ==> U(F\F) = ℕ.
>>
> Which just proves there is no necesary set.

Induction proves that there is no FISON that, when removed, changes the 
premise. Therefore all FISONs can be removed without changing the 
premise. The conclusion is U(F\F) = ℕ.

Regards, WM