Closed Interval

Last updated Nov 6, 2022

Let $(T, \leq)$ be a Total Ordering. An Closed Interval is $[a,b]$ for $a \leq b \in T$ is the Set $$[a,b] := {x \in T : a \leq x \leq b}$$

1. $[a, a] = {a}$ for $a \in T$.
2. Sometimes, when referring to an Closed Interval, we may include Closed Rays and $T$ itself.