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Path: ...!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> Newsgroups: sci.math Subject: Re: how Date: Tue, 11 Jun 2024 12:43:11 -0700 Organization: A noiseless patient Spider Lines: 93 Message-ID: <v4a9cg$16s49$4@dont-email.me> References: <qHqKnNhkFFpow5Tl3Eiz12-8JEI@jntp> <1OhEiVGoZeYKAlHf40u0M-DGu74@jntp> <65e48016-ecea-4832-bcdb-a5e3d94a66cd@att.net> <52y9XpKJ6QVz6e8s5Hvt4WK1nmE@jntp> <04ac4aa5-f508-40e1-b14f-0fa9883ac4c0@att.net> <-YYjghxYEV4-kYQzyEEkdPOmx9g@jntp> <d8638801-fa89-4764-ab60-90c690a4dc53@att.net> <cAb6HQm9T104zE20oIGGcWLO1Hk@jntp> <b6b4d308-15de-40e6-9311-d71ae43a32c3@att.net> <v42tme$2v0o0$1@dont-email.me> <H-DXrebldhGX0fN4NMx7hZyVGP0@jntp> <v47uvb$lh4k$3@dont-email.me> <v47vpf$lphl$1@dont-email.me> <v47vua$lh4c$3@dont-email.me> <v48141$lphl$2@dont-email.me> <v481od$lh4c$7@dont-email.me> <v4a98m$16s3t$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 11 Jun 2024 21:43:13 +0200 (CEST) Injection-Info: dont-email.me; posting-host="af7387139eef2adaeed8a4c9aa891781"; logging-data="1273993"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX182/aCQVAEw4SBf4Odhaj7isMxG9mpgF74=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:WYE87any55bsLQLrOvzcx5zHfNY= In-Reply-To: <v4a98m$16s3t$1@dont-email.me> Content-Language: en-US Bytes: 3495 On 6/11/2024 12:41 PM, Chris M. Thomasson wrote: > On 6/10/2024 4:20 PM, Chris M. Thomasson wrote: >> On 6/10/2024 4:09 PM, Moebius wrote: >>> Am 11.06.2024 um 00:49 schrieb Chris M. Thomasson: >>>> On 6/10/2024 3:47 PM, Moebius wrote: >>>>> Am 11.06.2024 um 00:33 schrieb Chris M. Thomasson: >>>>> >>>>>> Crap, or really bad? What did I miss here? >>>>> >>>>> Math? :-) >>>>> >>>> >>>> I was just thinking about, >>>> >>>> [1, 2, 3, 4, ...] >>>> >>>> applied to: >>>> >>>> [1/2, 2/2, 3/2, 4/2, ...] >>>> >>>> creates >>>> >>>> [.5, 1, 1.5, 2, ...] >>> >>> Ummm... >>> >>> [1/2, 2/2, 3/2, 4/2, ...] = [.5, 1, 1.5, 2, ...]. >>> >>> Say, in the context of Q or IR (with decinal representation of numbers). >>> >>>> Refining to all the naturals we get: >>>> >>>> [1, 2, ...] >>> >>> What do you "mean" be "refining"? :-P >>> >>> I guess you mean some sort of ""reduction"" (or "filtering"). >>> >>> Actually, I've never heard about this (in a math context). > > My programming side. ;^) > > >>> But it certainly can be defined. > > Yup! It sure can and is interesting to me. > > By the way... Wrt something like: > > 0.666... > > is: > > 0.(6) better and easier to read? > > >>> Let's call this operation "nat". >>> >>> Then >>> >>> nat [.5, 1, 1.5, 2, ...] = [1, 2, ...] . >>> >>> And, say, >>> >>> nat [.5, 2, 1.5, 7, ...] = [2, 7, ...] . >> >> >> For the filter, or refinement, yes. [.5, 2, 1.5, 7, ...] = [2, 7, ...] >> >> Indeed. >> >>> >>> Right? >>> >>>> Make any sense? >>> >>> Sure. >> > > Therefore: > > nat [-.5, 8/2, 14/3, 5/2, .6(6), 4/2, -7, 5.2, 0+0i, ...] = [4, 2, ...] > > The nat operation seems logical to me. :^) Or, if somebody desires to treat zero as a natural number the result would be, wrt the 0+0i element, [4, 2, 0, ...] Humm...