bashed it , can't find an elegant solution
consider the points Z, A=(Z-1), and a point B on the line OZ where ZB = 1 and Z is not between O an B.
If OB < OA let C be a point on OA such that OC = OB (case 1)
else let C be a point on OB such that OC = OA (case 2)
now, OA represents...