… okay? Yes? Nobody thought otherwise? Do we now have to clarify every statement about algebra by specifying that we’re talking about an algebra over the reals or the complex numbers? Or the polynomials or the p-adic integers, whose multiplications are also commutative?
No one would call these “n-dimensional” number systems either. The algebra for each of these operates in R1 and R2, respectively, but, like, you would describe their algebras as being over an n-dimensional vector space. It’s not wrong, but I don’t think “two-dimensional number system” is something you’d hear mathematicians say.
This pedantic aside feels so “I just watched a 3blue1brown video and feel verysmart™” that I don’t know what to do with it. It’s good to be interested in math, but this ain’t it. Everyone knew what they meant.
… okay? Yes? Nobody thought otherwise? Do we now have to clarify every statement about algebra by specifying that we’re talking about an algebra over the reals or the complex numbers? Or the polynomials or the p-adic integers, whose multiplications are also commutative?
No one would call these “n-dimensional” number systems either. The algebra for each of these operates in R1 and R2, respectively, but, like, you would describe their algebras as being over an n-dimensional vector space. It’s not wrong, but I don’t think “two-dimensional number system” is something you’d hear mathematicians say.
This pedantic aside feels so “I just watched a 3blue1brown video and feel verysmart™” that I don’t know what to do with it. It’s good to be interested in math, but this ain’t it. Everyone knew what they meant.