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Infinity is certainly not a real number, nor a complex number. There are plenty of systems (such as various compactions of the real or complex numbers, like th
by wnoise 16y ago
Infinity is certainly not a real number, nor a complex number. There are plenty of systems (such as various compactions of the real or complex numbers, like the Riemann sphere, or the surreal numbers) for which infinity is a member in good standing, and then there is no reason not to consider it a number.
- JadeNB 16y agoAlthough it's always dangerous to say to a mathematician something like “But there's no sense in which that's true!”, still I would be reluctant to refer to elements of the Riemann sphere as numbers; the sphere seems fundamentally a geometric rather than algebraic object (of course, until you start thinking of it as the complex projective ‘line’, at which point it becomes both :-) ). With that said, as I have argued elsethread, I certainly do think that there are occasions when infinity can be considered a number; the surreal numbers are an elegant example.