# Axiom:Points are Between Themselves

## Axiom

Let $\mathsf{B}$ be the relation of betweenness.

Let $=$ be the relation of equality.

Then the following axiom is imposed:

- $\forall a,b: a = b \implies \mathsf{B}aba $

where $a$ and $b$ are points.

## Intuition

If two points are the same, they are between themselves.

## 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 185 : Axiom $13$ (unnamed)