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: Thu, 20 Feb 2025 20:27:30 +0100
Organization: A noiseless patient Spider
Lines: 34
Message-ID: <vp7vn1$2vjvt$1@dont-email.me>
References: <vmo1bs$1rnl$1@dont-email.me> <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>
 <559d228c01ea290aec13e735ec85036862578165@i2pn2.org>
 <vp1lap$1l5b9$1@dont-email.me>
 <5220af0cb7d579f20d58809659d8dcb8d7ba046c@i2pn2.org>
 <vp28k5$1o28v$4@dont-email.me>
 <325c90249ce4a619cc8a7f7b19b4884d12bc58aa@i2pn2.org>
 <vp52ib$2bale$2@dont-email.me>
 <b90866f953ee17c5defdfd0a50e5ef89317b1a11@i2pn2.org>
 <vp70bo$2pd0f$2@dont-email.me> <75ad3257-06f3-4f71-99bf-82227ccadde2@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Thu, 20 Feb 2025 20:27:30 +0100 (CET)
Injection-Info: dont-email.me; posting-host="1a23733c4805074bd43b1a57ec6bff4b";
	logging-data="3133437"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19kzLxBUfEqBpkjesJy+Dyfykl7UoiRQwk="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:QdOXjYcAYBT/gInLHl7sGj+o2wY=
In-Reply-To: <75ad3257-06f3-4f71-99bf-82227ccadde2@att.net>
Content-Language: en-US
Bytes: 2672

On 20.02.2025 20:05, Jim Burns wrote:
> On 2/20/2025 5:32 AM, WM wrote:
>> On 20.02.2025 03:23, Richard Damon wrote:
> 
>>>
>>
>> Assume a set of sufficient FISONs.
> 
> == Assume S ⊆ {F} exists such that
> ⋃S is the only.inductive.subset of ⋃S
> 
>> |ℕ \ {1, 2, 3, ..., n}| = ℵo
>> is true for all FISONs.
> 
> Yes.
> 
> ⎛ For any two FISONs {i:i≤j} and {i:i≤k},
> ⎜ their sum {i:i≤j+k} is a FISON.

Yes.

>> That contradicts the assumption.
> 
> What is the assumption?

The assumption is the existence of S.
> 
> What is the contradiction?

The contradiction is that induction proves every FISON useless and 
therefore S  not existing.

Regards, WM