Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Sat, 19 Oct 2024 14:04:35 -0400 Organization: Peripheral Visions Lines: 30 Message-ID: References: <53460f91-4542-4a92-bc4b-833c2ad61e52@att.net> <29ce40e9-f18a-44d4-84d9-23e587cf9dea@att.net> <2b6f9104-a927-49ee-9cf0-6ee3f82edc23@att.net> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="utf-8"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 19 Oct 2024 20:04:44 +0200 (CEST) Injection-Info: dont-email.me; posting-host="fc53af885f7ba9a0343781612740b9c9"; logging-data="4192907"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18KR+1fBHzcXZ/quX4HqWSlrPmbrL8xNnY=" Cancel-Lock: sha1:fOO9Uei0xHoXgTbY9jGWmrQon7A= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 2834 WM has brought this to us : > On 19.10.2024 16:24, Alan Mackenzie wrote: >> WM wrote: > >>>> rather than the standard mathematical concept of a mapping from N -> N >>>> where n is mapped to 2n. In this standard notion, all numbers are >>>> doubled, and we encounter no undoubled even natural numbers. >> >>> Therefore the standard notion is wrong, if the natural numbers are a set. >> >> You mean it's wrong because it doesn't gel with your intuition? > > No, it does not comply with mathematics. When multiplying all natural numbers > by 2, then the number of numbers remains the same but the density is reduced > and therefore the interval is doubled. 2 > n. Hence either natural numbers > are created which have not been multiplied, then ℕ is not a set, or other > numbers are created, then ℕ is a set. > >> If you think you can obtain an >> "undoubled" number in that mapping, please feel free to give an example. > > I can prove it by 2n > n. > >> You can't, of course, you'll just say that all such are "dark numbers", > > Either dark numbers or natnumbers which have not been processed. There is no > other way because 2n > n. Processed? Created? As I told you before, these are objects not projects.