Open Ray

Last updated Nov 6, 2022

Let $(T, \leq)$ be a Total Ordering. An Open Ray is a Set $R \subset T$ of the form ${x \in T : x < a}$ or ${x \in T : x > a}$ for some $a \in T$.

1. We denote $(a, \rightarrow) := {x \in T : x > a}$ and $(\leftarrow,a) := {x \in T : x < a}$.