# Axiom:Symmetry of Equidistance

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## 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*(*Bull. Symb. Log.***Vol. 5**,*no. 2*: pp. 175 – 214) : p. $177$ : Axiom $1$