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: Sun, 26 Jan 2025 09:41:22 +0100
Organization: A noiseless patient Spider
Lines: 20
Message-ID: <vn4sfi$3ijdb$2@dont-email.me>
References: <vmo1bs$1rnl$1@dont-email.me>
 <ee4e189d-56bc-4ed7-b7b7-cd71fc4d2349@att.net> <vmqh9k$urua$1@dont-email.me>
 <903de8e1-3538-4cfe-9f7a-6509eda47ab6@att.net> <vmsvfv$1hn5k$1@dont-email.me>
 <3844edd7-0750-4418-bff6-2759817446b3@att.net> <vmvn1h$25r19$1@dont-email.me>
 <27377646-137a-4f8f-a7bb-a75707b2da96@att.net> <vn2gcf$2ouuo$2@dont-email.me>
 <965ee9868f28953d437113d0d38f069815499a3f@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 26 Jan 2025 09:41:23 +0100 (CET)
Injection-Info: dont-email.me; posting-host="f29b607f7791c09fbf29348f2e168486";
	logging-data="3755435"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/4WZopFpgwaN1jB+nMgbcNafmyZQycSE8="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:es6q82iCREru6vQzz2Gudo3Z6u0=
Content-Language: en-US
In-Reply-To: <965ee9868f28953d437113d0d38f069815499a3f@i2pn2.org>
Bytes: 2050

On 25.01.2025 14:56, joes wrote:

> There is obviously no single FISON that is equal to N.

Obviously every union of FISONs is finite, because there are never two 
consecutive actually infinite sets in ℕ, and every FISON has an infinite 
set as successors.

Obviously every unbion of FISONs is a FISON.
> 
>> Do you agree that or every FISON the question whether it is necessary
>> can be answered?
> Yes, in the negative. That does not imply the nonexistence of a
> sufficient set.

It implies that there is not a first FISON. That proves by induction 
that every FISON can be dropped. Your belief is dysfunctional logic.

Regards, WM