Interval Notation

Interval notation is a way of writing subsets of the real number line.

A closed interval is one that includes its endpoints: for example, the set {x | 3 x 1}.

To write this interval in interval notation, we use closed brackets [ ]:

[ –3, 1]

An open interval is one that does not include its endpoints, for example, {x | 3 x 1}.

To write this interval in interval notation, use parentheses:

( –3, 1)

You can also have intervals which are half-open and half-closed:

[ –2, 4)

You can also use interval notation together with the set union operator to write subsets of the number line made up of more than one interval: