Path: 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 20:53:43 +0200 Organization: A noiseless patient Spider Lines: 60 Message-ID: <100funo$1ous9$1@dont-email.me> References: <100a8ah$ekoh$1@dont-email.me> <100ccrl$upk6$1@dont-email.me> <100cjat$vtec$1@dont-email.me> <100fdbr$1laaq$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 19 May 2025 20:53:45 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f03bf24ea76c7f186b2b0e62e98ef69b"; logging-data="1866633"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18b8Cv1gFuHW7QePlw6cp3yzytDbpEhAZs=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:smnwTAquDEFsxj6269bAuwOswLE= Content-Language: en-US In-Reply-To: <100fdbr$1laaq$1@dont-email.me> On 19.05.2025 15:57, Mikko wrote: > On 2025-05-18 12:20:47 +0000, WM said: > >> On 18.05.2025 12:30, Mikko wrote: >>> On 2025-05-17 15:00:33 +0000, WM said: >>> >>>> 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. >>> >>> For example, if we pick 5 for n we have >>> >>> {1} >>> {1, 2} >>> {1, 2, 3} >>> {1, 2, 3, 4} >>> {1, 2, 3, 4, 5} >>> >>> then 6 and infinitely many other numbers are missing. So numbers >>> 6, and 7 are dark as are ingfinitely many other numbers. > >> Maybe for a 3-year old child. Doves can count to 7. Earthworms may >> fail at 1 already. > > Many animals can differentiate quantities up to about 7. As far as > we know most of them needn't and can't count. They just see the > difference. Accurate determination of larger quantities may require > counting. > > None of which is relevant to may observation that if n = 5 then your > definition makes 6 dark. If you have no idea of 6, it is dark for you. I you arbitrarily stop at 5 although you know 6, 5 is not dark for you. > >> It depends on the system. But important is that no system can get over >> the infinite gap of dark numbers. > > Why not? Cantor quite obviously gets over quite large infinities. Yes, but not by counting them one by one. He jumps to ω and can from there go on. He could also go back ω-1, ω-2, ... . But there is no finite initial segment reaching to ω/n for every n that has a finite initial segment. Let alone reaching to ω-n. Regards, WM >