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Path: ...!2.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: More complex numbers than reals? Date: Sun, 21 Jul 2024 15:56:31 -0700 Organization: A noiseless patient Spider Lines: 59 Message-ID: <v7k3n1$9id5$1@dont-email.me> References: <v6ihi1$18sp0$6@dont-email.me> <v6k3jb$1gjer$1@dont-email.me> <v6k56d$1gsq7$1@dont-email.me> <v6k6fb$1h0br$1@dont-email.me> <v6kcs2$1hehh$4@dont-email.me> <v6mugt$22opo$6@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Mon, 22 Jul 2024 00:56:33 +0200 (CEST) Injection-Info: dont-email.me; posting-host="e5e0901eabcdb6107cf2334f05523c53"; logging-data="313765"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18J+Jb/6chpaaPgSRsuAhDcu1LwlA3Px40=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:8ZY2NyXHok5JGCKdv9TDU1eMURE= Content-Language: en-US In-Reply-To: <v6mugt$22opo$6@dont-email.me> Bytes: 3002 On 7/10/2024 2:30 PM, Chris M. Thomasson wrote: > On 7/9/2024 3:16 PM, Moebius wrote: >> Am 09.07.2024 um 22:27 schrieb sobriquet: >> >>> How do you define sets exactly? >> >> Actually, we don't _define_ the concept of /set/ by a "proper >> definition". >> >>> Is there a specific set that corresponds to sqrt(2)? >> >> Well, rather a sequence (which is a certain kind of set in the context >> of set theory): >> >> (1, 1.4, 1.41, 1.414, ...) >> >>> Does this set have an infinite number of elements analogous to the >>> sqrt(2) having an infinite decimal expansion? >> >> Yes. See above. This sequence (called an /infinite sequence/) has >> infinitely many terms. >> >>> It seems that the existence of something like sqrt(2) is already >>> rather dubious. >> >> Oh, really? >> >> If you say so. >> >> So in your "math" there is no /number/ x such that x^2 = 2. >> >> Ok, if you can live with(out) that, fine. >> >>> In reality, things are finite and space and time might also be finite >>> (composed of atoms of space and time that can't be subdivided with >>> the parts retaining their original spatial and temporal properties). >> >> Yes, they could. >> >>> So if the concept of irrational numbers like sqrt(2) [etc.] >> >> Hint (1): You won't find numbers like sqrt(2) IN (PHYSICAL) REALITY. > > If we draw a unit square, sqrt 2 is in there by default, right? From the > unit square all other squares can be constructed. > > > >> >> Hint (2): You won't find numbers like 1, 2, 3 there neither/either (?). >> >> > Also, from the unit circle, all circles and ellipses can be created. The ellipse aspect is that of a circle rotated in 3d is an ellipse when viewed on the projected plane. Check this out in VR: https://skfb.ly/6RozT