---- > [!definition] Definition. ([[ray]]) > If $X$ is an [[strict order relation|ordered set]], and $a \in X$, there are fourier subsets of $X$ that are called the **rays** determined by $a$. They are: $\begin{align} (a, +\infty) :=& \{ x : x > a \} \\ (-\infty , a) :=& \{ x : x < a \} \\ [a, +\infty) :=& \{ x : x \geq a \} \\ (-\infty, a] :=& \{ x : x \leq a \}. \end{align}$ \ Sets of the first two types are called **open rays**, while sets of the last two types are called **closed rays**. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```