# Question #2136e

Oct 20, 2016

Closed interval: specified end points are included.
Open interval: specified end points are not included.
Half-open = half-closed interval: one of the specified end point is included but not the other.

#### Explanation:

An interval is identified by specifying the end point values of the interval.

It may be written (for example) as something like:
$\textcolor{w h i t e}{\text{XXX}} x \in \left[4 , 7\right]$
This is an example of a closed interval which indicates that $x$ could be $4$, or any value between $4$ and $7$, or $7$.

As an alternative we might have:
$\textcolor{w h i t e}{\text{XXX}} x \in \left(4 , 7\right)$
which is an open interval which indicates that $x$ could be any value between $4$ and $7$ but not $4$ or $7$.

A half-open interval might look like
$\textcolor{w h i t e}{\text{XXX}} x \in \left(4 , 7\right]$
...any value greater than but not equal to $4$ up to and including $7$
or
$\textcolor{w h i t e}{\text{XXX}} x \in \left[4 , 7\right)$
...which would include $4$ but exclude $7$