Betweenness

Summary

Betweenness is the relation "the point $y$ lies between the points $x$ and $z$". In an affine space over an ordered field it means that $y$ lies on the segment from $x$ to $z$. In axiomatic geometry it is a primitive relation, and the axioms of order, such as Pasch's axiom, describe it. Segments, rays, half-planes and the inside of a triangle are all defined from it.