direction

[sadhu]

what is the mathematical definition of direction ?

is it always associated with movement or transfer ?

if not then what is the meaning of initial and final point in the definition of directed line segment?

[HallsofIvy]

Since neither movement nor transfer is a "mathematical term", no, direction is not mathematically defined in terms of them. "Direction" is defined as a ray- that part of a line segment on one side of a given point. Of course, "on one side of" is just defined as "a point divides a segment into two parts: choose either of them."

I apparently don't understand your last question. I don't see what it has to do with "if not". A "directed" line segment starts with a line segment. Then you choose one of the end points as the 'base' for the ray that determines the direction. Neither movement nor transfer required there.