On 07/05/2013 08:48, William Elliot wrote: > Let C be a collection of n points with the property that > any line L with two points of C on it, has a third point > of C on it. > > How is it that C is collinear, ie all points of C are > on a single line?

The assertion is not true if points are allowed to be coincident. For example P1 = (0,0) P2 = (1,0) P3 = (2,0) P4 = P5 = P6 =(1,1)