Definition:Strictly Between

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Let $a, b, c \in S$ such that $a \prec b$ and $b \prec c$.

That is, such that:
 * $a \preceq b$ and $a \ne b$
 * $b \preceq c$ and $b \ne c$

Then $b$ is strictly between $a$ and $c$.

Also see

 * Definition:Between