# Axiom:Symmetry of Equidistance

## Contents

## 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

- June 1999: Alfred Tarski and Steven Givant:
*Tarski's System of Geometry*(*The Bulletin of Symbolic Logic***Vol. 5**,*no. 2*: 175 – 214) : Page 177 : Axiom $1$