Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Mon, 21 Oct 2024 00:37:43 -0700 Organization: A noiseless patient Spider Lines: 14 Message-ID: References: <3f5fcf13171337f1c3d2ef84cc149be327648451@i2pn2.org> <97b84c07aa526903a0788584f7f7ae9121f8b81f@i2pn2.org> <60f1280e-e226-4314-8eca-da5410be8ca3@tha.de> <96a7aa944085e76faed69c8db9a8dca599e1a159@i2pn2.org> <7d314712-c5b5-4dfc-af61-3885ccf1c771@tha.de> <9f1304bb-8f8d-46ab-adec-592f1fc549d2@tha.de> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 21 Oct 2024 09:37:44 +0200 (CEST) Injection-Info: dont-email.me; posting-host="c770b3133348e91147f2be2370fb578a"; logging-data="919254"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18Le7ZAVGAqHGgGBHXERGHKGrUYmmrIRQE=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:pIkYMu7wbGZjZ1ZHOPemT4LAQwY= In-Reply-To: <9f1304bb-8f8d-46ab-adec-592f1fc549d2@tha.de> Content-Language: en-US Bytes: 2639 On 10/21/2024 12:14 AM, WM wrote: > On 21.10.2024 01:04, joes wrote: >> Am Sat, 19 Oct 2024 10:23:05 +0200 schrieb WM: > >>> That is not possible if all natural numbers are doubled. The result >>> covers the interval (0, ω*2) twice as large as the original one (0, ω). >> This destroys the ordering. If m>n, then 2m>2n. > > No, also the transfinite numbers are ordered. But for dark numbers the > ordering is inaccessible anyhow. Why are the dark numbers unordered? is n + say_anything_that_is_greater_than_zero, unordered where n can be > the result?