Rays

Definition: Ray

Let $S$ be a set with a total order $\le$ and a strict total order $<$.

Each $a\in S$ defines the following rays:

• $(-\infty ;a)\stackrel{\text{def}}{=}\{s\in S\mid s<a\}$
• $(-\infty ;a]\stackrel{\text{def}}{=}\{s\in S\mid s\le a\}$
• $(a;+\infty )\stackrel{\text{def}}{=}\{s\in S\mid a<s\}$
• $[a;+\infty )\stackrel{\text{def}}{=}\{s\in S\mid a\le s\}$