Comment by yifanl
13 days ago
Notably, neither `1 + i > 1 - i` or `1 + i < 1 - i` are correct statements, and obviously `1 + i = 1 - i` is absurd.
13 days ago
Notably, neither `1 + i > 1 - i` or `1 + i < 1 - i` are correct statements, and obviously `1 + i = 1 - i` is absurd.
What do > and < mean in the context of an infinite 2D plane?
Typically, the order of complex numbers is done by projecting C onto R, i.e. by taking the absolute value.
Yes I’m aware. It’s a work around but doesn’t give you a sensible ordering the way most people expect, i.e:
-2 > 1 (in C)
Which is why I prefer to leave <,> undefined in C and just take the magnitude if I want to compare complex numbers.
One is above the plane and the other is below it. ;)
In a word - "true".
In more words - it's interesting, but messy:
https://en.wikipedia.org/wiki/Partial_order
https://en.wikipedia.org/wiki/Ordered_field
> The complex numbers also cannot be turned into an ordered field, as −1 is a square of the imaginary unit i.