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Let $B$ be a strict betweenness relation. In the following the sets $B_{*pq}, B_{p*q}, B_{pq*}, B_{pq}, B(p,q)$ are defined in the entry about some theorems on the axioms of order.
Theorem 1 Three elements are in a strict betweenness relation only if they are pairwise distinct.
Theorem 2 If $B$ is strict, then $B_{*pq}$ $B_{p*q}$ and $B_{pq*}$ are pairwise disjoint. Furthermore, if $p=q$ then all three sets are empty.
Theorem 3 If $B$ is strict, then $B_{pq}\cap B_{qp}=B_{p*q}$ and $B_{pq}\cup B_{qp}=B(p,q)$
Theorem 4 If $B$ is strict, then for any $p,q\in A$ $p\ne q$ $B_{*pq}$ $B_{p*q}$ and $B_{pq*}$ are infinite.
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