Nicholas Clark wrote:
Jonathan Lang wrote:
> They can be:
>
> $A > $B if $A.x > $B.x | $A.y > $B.y;
> $A < $B if $A.x < $B.x | $A.y < $B.y;
>
> This also allows you to unambiguously order any arbitrary set of
> complex numbers.
If I'm reading that correctly then there are values of $A and $B for which
$A > $B and $A < $B are simultaneously true.
Good point. What I meant to say was:
$A > $B if $A.x > $B.x | $A.x == $B.x & $A.y > $B.y;
$A < $B if $A.x < $B.x | $A.x == $B.x & $A.y < $B.y;
Or, in polar coordinates,
$A <= $B if pi/2 < ($A - $B).a < 3*pi/2;
With the other three comparisons defined relative to that. In effect,
anything that's anywhere to the east of A, as well as anything that's
due north of it, counts as being greater than it.
--
Jonathan "Dataweaver" Lang
