Axiom:Reflexivity of Betweenness
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Axiom
Let $\mathsf{B}$ be the relation of betweenness.
Then the following axiom is imposed:
- $\forall a, b: \mathsf{B}abb$
where $a$ and $b$ are points.
Intuition
The endpoint of a line segment is on the line segment.
Sources
- June 1999: Alfred Tarski and Steven Givant: Tarski's System of Geometry (Bull. Symb. Log. Vol. 5, no. 2: pp. 175 – 214) : p. $185$ : Axiom $12$