[(65, 92)]
For real numbers $a,b$, an interval between $a$ and $b$ is a subset of $\mathbb{R}$1 containing all of the real numbers between $a$ and $b$. An interval is of one of the following forms, depending on which of the two endpoints (i.e., $a$ and $b$) it contains:
- The open interval, denoted $(a,b)$, is the set of real numbers containing all real numbers between $a$ and $b$, not including $a$ and $b$: $$ \begin{align} (a,b) := \{x \in \mathbb{R}: a < x < b \} \end{align} $$
- The closed interval, denoted $[a,b]$, is the set of real numbers containing all real numbers between $a$ and $b$, including both $a$ and $b$: $$ \begin{align} [a,b] := \{x \in \mathbb{R}: a \leq x \leq b \} \end{align} $$
- The half open intervals, denoted $(a,b]$ and $[a,b)$, are the sets of real numbers containing all real numbers between $a$ and $b$, including one of $a$ and $b$ and not the other: $$ \begin{align} (a,b] &:= \{x \in \mathbb{R}: a < x \leq b \} \\ [a,b) &:= \{x \in \mathbb{R}: a \leq x < b \} \end{align} $$