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: More complex numbers than reals? Date: Tue, 9 Jul 2024 12:17:05 -0700 Organization: A noiseless patient Spider Lines: 38 Message-ID: References: <87msmqrbaq.fsf@bsb.me.uk> <0dUETcjzkRZSIY0ZGKDH2IRJuYQ@jntp> <87v81epj5v.fsf@bsb.me.uk> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 09 Jul 2024 21:17:06 +0200 (CEST) Injection-Info: dont-email.me; posting-host="ce358e0d0d9664a700ff455d87f9b3cd"; logging-data="1579963"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19XXcTcLjM3IOwL/odsSmwjPAeEQ9nMZtE=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:Yqx4+iEtwPPlX2BeRdNbSBFAv2c= Content-Language: en-US In-Reply-To: Bytes: 2483 On 7/9/2024 12:11 PM, Chris M. Thomasson wrote: > On 7/9/2024 10:30 AM, Ben Bacarisse wrote: >> WM writes: >> >>> Le 09/07/2024 à 14:37, Ben Bacarisse a écrit : >>> >>>> A mathematician, to whom this is a whole new topic, would start by >>>> asking you what you mean by "more".  Without that, they could not >>>> possibly answer you. >>> >>> Good mathematicians could. >>> >>>>   So, what do you mean by "more" when applied to >>>> sets like C and R? >>> >>> Proper subsets have less elements than their supersets. >> >> Let's see if Chris is using that definition.  I think he's cleverer than >> you so he will probably want to be able to say that {1,2,3} has "more" >> elements than {4,5}. >> > > I was just thinking that there seems to be "more" reals than natural > numbers. Every natural number is a real, but not all reals are natural > numbers. > > So, wrt the complex. Well... Every complex number has a x, or real > component. However, not every real has a y, or imaginary component... To refine it... NO Real has a y, or imaginary component. The complex numbers do. So, can be thought of as being more dense? Or space filling a 2d plane? Reals are 1d. Is 2d "denser" than 1d? Or is that the wrong way to think about it? Thanks. > > Fair enough? Or still crap? ;^o