Axiom:Symmetry of Betweenness

Axiom

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

Then the following axiom holds:

$\forall a, b, c: \mathsf{B}abc \implies \mathsf{B}cba$

where $a, b, c$ are points.

Intuition

If a point is on a line segment, it is still on the line segment if you traverse it from the other direction.

Sources

• June 1999: Alfred Tarski and Steven Givant: Tarski's System of Geometry (Bull. Symb. Log. Vol. 5, no. 2: pp. 175 – 214) : p. $185$ : Axiom $14$