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I vote for “complete” numbers in place of “complex”, and we just don’t reference “imaginary” at all — it goes from “real” to “complete” when you add the missing
by zmgsabst 5y ago
I vote for “complete” numbers in place of “complex”, and we just don’t reference “imaginary” at all — it goes from “real” to “complete” when you add the missing root of unity.
- charcircuit 5y agoHow are imaginary complete? It's not hard to make a superset of the complex numbers.
- openfuture 5y agoalgebraically, see: fundamental theorem of algebra (proved by Gauss in his PhD thesis)
- charcircuit 5y agoWhat's your point? You can define some other property which complex numbers don't satisfy.
- openfuture 5y agoSure. What is my burden of proof exactly?
- zmgsabst 5y ago
- zwkrt 5y agoMy vote as an amateur mathematician would be “rotational” numbers. Everything having to do with complex numbers secretly (or not so secretly) has to do with angles and rotations, and it would be easy to describe to a class of middle schoolers that if you want to do math to describe how things rotate, it makes sense that you need a 2D space.
- abecedarius 5y agoTwirly numbers, to me.
- deleted 5y ago[deleted]
- hammock 5y agoThis just made it click for me why imaginary numbers are used in electrical engineering
- jacobolus 5y agoTristan Needham’s word is “amplitwist”, meaning a scaling composed with a planar rotation. A complex number should be thought of as the quotient of plane vectors: a quantity z = v/u which when multiplied by vector u yields v: that is zu = v. (Important note: multiplication of a complex number by a vector is not commutative, zu ≠ uz.) For more: http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
- fsloth 5y agoWell, IMO their rotational feature is kind of the accidental, happy and mysterious side-effect that starts from the "simple" computational trick of defining sqrt(-1) being i, and taking the calcuslations from there. I would philosophically say "Completeness" is a more important property (since now negative roots have a meaning attached to them). But their rotational aspect is perhaps more mind blowing.
- zwkrt 5y agoI disagree but I don’t have an incredibly concrete argument, only an intuition that in the case of complex numbers, our mathematical formalism for solving equations proceeded our mathematical intuition about cyclical processes.
- zodiac 5y agoBut "completeness" already has a (different) definition, like when we say the reals are complete but the rationals are not edit: to match with existing terminology you might call the reals the "completes" and the complex numbers the "algebraically-closeds" but... meh.
- zmgsabst 5y ago