interval

We can perform the same operations on intervals as we can on sets:

Intervals and set operations

$[1,3]\cup [2,5]=[1,5]$
$[1,3]\cap [2,5]=[2,3]$
$[1,3]\setminus [2,5]=[1,2)$
$\mathbb{R}\setminus (-1,1]=(-\infty ,-1]\cup (1,\infty )$

Note: $\infty$ can never be included in an interval, it’s just implicitly there so e.g. $[1,\infty )=\{x\in \mathbb{R}\mid x\ge 1\}$.

Note: The union of two intervals is not necessarily an interval, e.g. $[1,2]\cup [10,20]$ is not an interval.