Comment by SyzygyRhythm
12 days ago
Is it two, or is it infinite? The quaternions have three imaginary units, i, j, and k. They're distinct, and yet each of them could be used for the complex numbers and they'd work the same way. How would I know that "my" imaginary unit i is the same as some other person's i? Maybe theirs is j, or k, or something else entirely.
It's 2 because there cannot be just one. There must be 2. Same as with magnetic poles and Siths. (and not same as with Highlanders.)
It's not infinite, because if you add more, you get a different space of numbers.
j and k are not complex numbers, in the same way that i is not a real number.
Changing the name of a number doesn't change the number. "Two" is not a different number from "2".