Re:Code is run more than read
by bruce343434 on Friday December 01, 2023 @03:34AM
(#38484520)
But |5|=|-5| so I don't exactly see your point.
Edit: oh, I see what you mean. 1 is not larger or smaller than i, but it also doesn't equal i.
This is just imposing an chosen (and in this case, pretty natural) order on a set without total order. But as you note, you have to give something up. In this case the order identifies each number on a circle in the complex plane with a single value, their magnitude.
I've never really seen this notation used, but it could have some use in partially-ordered sets.
Now if you really think about, a number of a given magnitude on x axis also isn't exactly "equal" to a name of same magnitude on y axis or vice versa. Other wise, -5 and 5 should be equal, because they're the same magnitude from 0.