Definition:Real Interval/Unbounded Closed

Definition
There are two unbounded closed intervals involving a real number $a \in \R$, defined as:


 * $\left [{a \,.\,.\, \to} \right) := \left\{{x \in \R: a \le x}\right\}$


 * $\left ({\gets \,.\,.\, a} \right] := \left\{{x \in \R: x \le a}\right\}$

Also denoted as
The notation using $\infty$ is usual:
 * $\left [{a \,.\,.\, \infty} \right) := \left\{{x \in \R: a \le x}\right\}$


 * $\left ({-\infty \,.\,.\, a} \right] := \left\{{x \in \R: x \le a}\right\}$

On the $\gets \cdots \to$ notation is preferred.

Also see

 * Definition:Open Real Interval
 * Definition:Closed Real Interval
 * Definition:Half-Open Real Interval
 * Definition:Unbounded Open Real Interval