Axiom:Symmetry of Equidistance

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Axiom

Let $\equiv$ be the relation of equidistance.


Then the following axiom holds:

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

where $a$ and $b$ are points.


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".


Sources