Axiom:Symmetry of Equidistance
Then the following axiom holds:
- $\forall a,b: ab \equiv ba$
where $a$ and $b$ are points.
Note on Name
Although the name of this axiom is given in the original publication as "Reflexivity Axiom for Equidistance", it is clear from the definitions of a reflexive relation and a symmetric relation that it really ought to be named the "Symmetry Axiom for Equidistance".