Definition:Real Interval/Unbounded Open

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

Using the same symbology, the set $\R$ can be represented as an unbounded open interval with no endpoints:


 * $\openint \gets \to = \R$

Also denoted as
The notation using $\infty$ is usual:

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

Also known as
Some sources refer to these as open infinite (real) intervals.

Also see

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