Show that the real projective line, P1, is orientable

Question

I'm asked to show that the real projective line, P1, is orientable. I'm not quite sure how to define orientable to prove this.

Thanks.

Answer 1

By one point $P$, a projective line is not divided into two segments.
Only two point $P, Q$ divide it into two segments.
A third point $R$ lies in one of these two segments.
This is the concept of orientation or simply direction on the line: there are two possibilities of the order of the points, namely: $PRQP$ or $PQRP$.
Draw the line e.g. as a circle to illustrate this.