Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.logic Subject: Re: Simple enough for every reader? Date: Mon, 19 May 2025 20:44:10 +0200 Organization: A noiseless patient Spider Lines: 40 Message-ID: <100fu5r$1oqf5$1@dont-email.me> References: <100a8ah$ekoh$1@dont-email.me> <878qmt1qz6.fsf@bsb.me.uk> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 19 May 2025 20:44:12 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f03bf24ea76c7f186b2b0e62e98ef69b"; logging-data="1862117"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/SpJlt6cNtsmkecOlYdcigFIJSvKto4ts=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:2CwxCMJ4UijBAJQ9M4JYHQbMM4w= Content-Language: en-US In-Reply-To: <878qmt1qz6.fsf@bsb.me.uk> Bytes: 2092 On 19.05.2025 00:41, Ben Bacarisse wrote: > WM writes: > >> Are you aware of the fact that in >> >> {1} >> {1, 2} >> {1, 2, 3} >> ... >> {1, 2, 3, ..., n} >> ... >> >> up to every n infinitely many natural numbers of the whole set >> >> {1, 2, 3, ...} >> >> are missing? Infinitely many of them will never be mentioned >> individually. They are dark. > > Presumably you are aware that for every n in ℕ, n will be mentioned in > infinitely many such sets? For every n that can be mentioned. > They are bathed in light. {1} has infinitely many (ℵo) successors. If {1, 2, 3, ..., n} has infinitely many (ℵo) successors, then {1, 2, 3, ...., n, n+1} has infinitely many (ℵo) successors. For every n that can be defied. See? But you are too biased and fanatic to accept mathematical proof by induction. > > Do they still let you teach this stuff? I am one of the few Professors worldwide who do teach the correct view of infinity (if actual infinity exists at all). Regards, WM