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[18.26.2.123]) by smtp.gmail.com with ESMTPSA id o18-v6sm7333803qki.38.2018.08.31.13.30.47 (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Fri, 31 Aug 2018 13:30:47 -0700 (PDT) In-Reply-To: <20180831195942.GA4898@ACM> Content-Language: en-GB X-detected-operating-system: by eggs.gnu.org: Genre and OS details not recognized. X-Received-From: 2607:f8b0:400d:c0d::235 X-BeenThere: emacs-devel@gnu.org X-Mailman-Version: 2.1.21 Precedence: list List-Id: "Emacs development discussions." List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: emacs-devel-bounces+ged-emacs-devel=m.gmane.org@gnu.org Original-Sender: "Emacs-devel" Xref: news.gmane.org gmane.emacs.devel:229148 Archived-At: Hey Alan, On 2018-08-31 15:59, Alan Mackenzie wrote: > I'm speaking not as a mathematician, but as somebody with a degree in > maths. I'm speaking as someone who didn't expect a conversation like this one to spark such a strong-worded discussion :) The whole debate rings odd to me (I agree with https://math.stackexchange.com/questions/36289/is-infinity-a-number: It comes down to the definition of "number," as well as the definition of "infinity") > +/-infinity are not numbers. They do not satisfy the axioms which > define numbers. For example they do not satisfy > > (x + y) + z = x + (y + z) > > . They cannot be made to satisfy these axioms. I see the point, but… floating point numbers are not associative either, and it doesn't seem to controversial to call them "numbers". >> They're not real numbers, but neither are complex numbers, >> split-complex numbers, dual numbers, p-adic numbers, quaternions, >> octonions, sedenions, hyperreal numbers, or (please no) surreal >> numbers. > > That's a strawman. The issue being discussed here is numbers, not > arbitrary algebraic structures. I read this as an example of the many meanings that the word "number" can take, depending on the context. It sounded pretty convincing. >> .... she has no exclusive claim over the definition (such as it is) of >> "number" > > That's analagous to saying that climate scientists don't have the > exclusive say-so about climate change. Ha ha, who needs experts? This is a very strongly worded charge. The original formulation could have been better, but to me it didn't look like a rejection of expertise… rather, I took it as a statement that the word "number" gets assigned different meanings across fields. >> (and I'm a bit surprised if she hadn't heard of at least one of the >> extended real lines I linked). > > Again, offensive. "Infinity", with or without a sign, might be classed > as an "extended number", but as noted above, is not a number. I don't understand this part. Does the word "number" on its own even have a strict definition, beyond something vague like Wikipedia's "mathematical object used to count, measure and also label"? Cheers, Clément.