In mathematics, a separation relation is a formal way to arrange a set of objects in an unoriented circle.
In this way it is a final, further weakening of the concepts of a betweenness relation and a cyclic order.
There is nothing else that can be forgotten: up to the relevant sense of interdefinability, these three relations are the only nontrivial reducts of the ordered set of rational numbers.
[2] The separation may be used in showing the real projective plane is a complete space.
[3] The relation of separation of points was written AC//BD by H. S. M. Coxeter in his textbook The Real Projective Plane.