Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: The set of necessary FISONs Date: Mon, 27 Jan 2025 12:13:38 +0100 Organization: A noiseless patient Spider Lines: 19 Message-ID: References: <903de8e1-3538-4cfe-9f7a-6509eda47ab6@att.net> <3844edd7-0750-4418-bff6-2759817446b3@att.net> <27377646-137a-4f8f-a7bb-a75707b2da96@att.net> <965ee9868f28953d437113d0d38f069815499a3f@i2pn2.org> <2f3fb91b5a9c930c3a43d1f51de2813df566ab6d@i2pn2.org> <82d149d0729cf982ded3ec719c4f83034b1c95f3@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 27 Jan 2025 12:13:38 +0100 (CET) Injection-Info: dont-email.me; posting-host="070749b6ef36b80f3e85f929ce6d891c"; logging-data="865116"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/xFrEnKsg0hAye/+HeRkHyK7vk74dOIAc=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:Bh1kpZbt8/4IVT6LZeckm09Nbow= In-Reply-To: <82d149d0729cf982ded3ec719c4f83034b1c95f3@i2pn2.org> Content-Language: en-US Bytes: 2258 On 26.01.2025 20:06, joes wrote: > Am Sun, 26 Jan 2025 19:08:08 +0100 schrieb WM: >>>> But no actually infinite set is possible. >>>> {1} >>>> {2, 1} >>>> {3, 2, 1} >>>> ... >>>> The length of the first column gives the cardinality. >>> The length? You gave an infinite list. Every column is infinite. >> No row is infinite. No column is longer than all rows. All rows and >> columns belong to potentially infinite collections. > All columns are infinite. No column is greater than all rows. All rows are finite. No column is actually infinite, i.e., has length |ℕ|. Regards, WM