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I get what you're saying, but complex numbers go right into literally any slot a real number goes into. That isn't true of a matrix. Plus, they implicitly inclu
by ravi-delia 5y ago
I get what you're saying, but complex numbers go right into literally any slot a real number goes into. That isn't true of a matrix. Plus, they implicitly include the reals as a subset, which lets them follow in the tradition of the integers, rationals, and reals. It's sort of hazy, but I'd only start to draw the line at the p-adiacs.
- mihaic 5y agoIt is a bit hazy, yes. For me having a total order relationship is one of the intrinsic properties of intuitive numbers. Complexes don't have that, but reals do, so I'm sure if you meant you can put them in the slot, but you'd compare the modulus. That's why I'd prefer to relabel them like "2-d numbers" for instance, to make it clear that some properties are affected like going from points on a line to points on the plane.
- ravi-delia 5y agoThat's a super fair point. I guess to me it matters more that it has all the usual field behaviors with the reals as a subset, but it is the first step "up" the hierarchy where you lose something instead of just gaining. I'm sort of used to substituting a metric in for order, but that obviously doesn't work everywhere.