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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:

[ 4 , 2 ] ( 1 , 1 ) ( 1 , 2 ] { 4 }