Darren Duncan wrote: >> Side note: one thing that I recently learned concerning implication >> operators is that the direction of the implication doesn't necessarily >> follow the direction of the arrow. In particular, "A if B" is "A←B", >> and "A only if B" is "A→B": in both of the original statements, the >> implication flows right to left. > > I thought that the direction did matter, and that's why there are distinct > versions in each direction. It's like how < and > are the same thing but > with the direction reversed, or subset/superset or contains/contained-by. > > If you read "A → B" as "A implies B" then that's the same as "if A then B", > then the cause-effect reads left to right, which does follow the direction > of the arrow, like Perl's "if cond() then action()".
The point is that it's equally valid to read "A → B" as "A only if B", with the cause-effect going from B to A. You have the same truth table for both "A only if B" and "if A then B", so they use the same logical operator; but the cause/effect flow is reversed between them. -- Jonathan "Dataweaver" Lang
