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 non-existence of "dark numbers" Date: Tue, 18 Mar 2025 11:07:22 +0100 Organization: A noiseless patient Spider Lines: 15 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 18 Mar 2025 11:07:22 +0100 (CET) Injection-Info: dont-email.me; posting-host="ac4a04604081f55585198279358e958d"; logging-data="2341063"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/wAw4DLFbUz4uM/Ehi02wlKTPwmmx5DgQ=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:CWKDanB4Vsy4EP8ZPU5bukCruOE= Content-Language: en-US In-Reply-To: Bytes: 2282 On 18.03.2025 10:56, FromTheRafters wrote: > on 3/18/2025, WM supposed : >> The set is ordered and if it is actually infinite, then all its >> elements are there and  do not appear from nothing but then it has a >> greatest element. > > Nope, it is a limit ordinal. All elements of ℕ are there. That is the assumption. If no greatest can be identified, then the reason are dark numbers. Otherwise only potential infinity could solve the dilemma. Regards, WM