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()".

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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