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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: Tue, 28 Jan 2025 23:07:19 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <4168e1e05c658fd9f96b4550c12f4dfec28ca843@i2pn2.org> 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> <vn4sfi$3ijdb$2@dont-email.me> <e51fcde5622ccc6beab7882831e5f7033c04d150@i2pn2.org> <vn5gur$3qu1c$3@dont-email.me> <77fb6230f3ef78f7524b70785c4772313e238258@i2pn2.org> <vn7r2r$q7sl$2@dont-email.me> <814297ada299a65bb9f427ddec5646afcc94be9f@i2pn2.org> <vn85es$u7pk$2@dont-email.me> <6403f6e569f236f2609dbfdfb6c676981453cf77@i2pn2.org> <vna7ig$1ng1j$4@dont-email.me> <0a864672c83f67003c62d86d02b93ad55fd0be94@i2pn2.org> <vnasne$1s6hg$4@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Wed, 29 Jan 2025 04:07:20 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1645358"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird X-Spam-Checker-Version: SpamAssassin 4.0.0 In-Reply-To: <vnasne$1s6hg$4@dont-email.me> Content-Language: en-US On 1/28/25 10:22 AM, WM wrote: > On 28.01.2025 13:45, Richard Damon wrote: >> On 1/28/25 4:21 AM, WM wrote: >>> On 28.01.2025 00:32, Richard Damon wrote: >>>> On 1/27/25 9:33 AM, WM wrote: >>> >>>>> Also an infinite set needs a first element. But no FISON is >>>>> necessary or sufficient. >>> >>>> Which means the set of "necessary FISONs" doesn't exist. >>> >>> The set of useful FISONs does not exist. Otherwise name the first one. >> >> You need to define "useful". > > A FISON is useful if its removal changes the union. > > Regards, WM So, you agree then that you whole concept of FISONs are not useful when you start from the infinite set of them. OF course, the start of your problem is that your logic can't make that infinite set in the first place to work at removing any from the set. Sorry, you are just proving your stupidity.