Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Mon, 17 Feb 2025 22:02:20 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <559d228c01ea290aec13e735ec85036862578165@i2pn2.org>
References: <vmo1bs$1rnl$1@dont-email.me> <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$4@dont-email.me>
 <f85884a59c9301bfc9d6a66fa935b74dc080ff24@i2pn2.org>
 <vot40r$lfa0$2@dont-email.me>
 <865ffa4c4c1091981c5b3b93ddf3dba690cd5ad2@i2pn2.org>
 <vp02g2$188u2$7@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 18 Feb 2025 03:02:20 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="559652"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
Content-Language: en-US
X-Spam-Checker-Version: SpamAssassin 4.0.0
In-Reply-To: <vp02g2$188u2$7@dont-email.me>

On 2/17/25 2:25 PM, WM wrote:
> On 16.02.2025 19:39, Richard Damon wrote:
>> On 2/16/25 11:33 AM, WM wrote:
>>> On 16.02.2025 13:11, joes wrote:
>>>> Am Sun, 16 Feb 2025 11:39:45 +0100 schrieb WM:
>>>
>>>>> Therefore all can be removed, and U(F) = ℕ ==> U(F\F) = ℕ.
>>>> No, obviously you can’t remove all
>>>
>>> Proofs by induction cover all elements of the set. My proof proves 
>>> that no FISON is capable of changing the premise UF = ℕ.
> 
>> There is no requirement for a "necessary" elememt for the set.
> 
> A set without elements is an empty set and not capable of producing ℕ.
> 
> Regards, WM
> 

But an empty set of REQUIRED elements doesn't mean we can't have a set 
of sufficient elements.

There is no requirment for a set of required digits, if we have options, 
which we do.

We can use all sorts of infinite sets to build the set of Natural Numbers.

In fact, we have so many options we can't count them.