4 ms·
Think how any number on the z axis of complex plain isn't equal to the a number of same magnitude, on x and y axis. Now if you really think about, a number of
by omeid2 3y ago
Think how any number on the z axis of complex plain isn't equal to the a number of same magnitude, on x and y axis.
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.
- bruce343434 3y agoBut |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.
- ska 3y agoThis 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.
- omeid2 3y agoIt is formalisms all the way down.