Axiom:Symmetry of Equidistance

Axiom
Let $a$ and $b$ be points.

Let $\equiv$ be the relation of equidistance.

Then the following axiom is imposed:


 * $\forall a,b: ab \equiv ba$

Intuition
The length of a line segment is not dependent on which end you start measuring.

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".