Axiom:Density of Betweenness

Axiom
Let $\mathsf{B}$ be the relation of betweenness.

Let $\ne$ be the relation of being distinct.

Then the density of betweenness is expressed by the statement:


 * $\forall a,b: \exists c: a \ne b \implies c \ne a \land c \ne b \land \mathsf{B}acb$

where $a,b,c$ are points.

Intuition
Between any two distinct points you can draw a third point, distinct from both.