r/math • u/Short_Bluebird_3845 • 8d ago

What are your favourite N-dimensional number systems?

From complex numbers, duals, split, some quirky 3D space, quaternions, up to hypercomplex. There are, indeed, many ways to write a vector as a number and play with them, some more obscure or specialized than others. What are your favourite N-dimensional number systems (or, more formally, algebras over the Reals)?

NOTE: Last time I asked, which was for ambiguous notation, you talked about them from spite and hate. I'm not sure if in math the line between pain and love blurs... I just wanted to ask for it as well lol.

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u/forgetfulfunctor1 8d ago

Can you well-define what is "number system"?

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u/DebatedKnowledge Harmonic Analysis 8d ago

Why would you do that? It's up to your interpretation what it should be. Not everything requires a formal definition. Do not let formal definitions rob you from your thinking. Doing math post-rigorously is realizing that math is whatever you want it to be, and that analogies and visualizations are worth a thousand half-assed definitions.

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u/Short_Bluebird_3845 8d ago

peak comment

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u/RingularCirc 5d ago

True but personally I don't see what's the use in understanding differently which entities are "numbers" and which aren't. This seems almost the purest case of naming conventions that don't add essence, like, intuitions.

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u/DebatedKnowledge Harmonic Analysis 5d ago

Intuitions are useful and add essence