# Interval Notation

From WeBWorK

#### Using Interval Notation

- If an endpoint is included, then use
`[`or`]`. If not, then use`(`or`)`. For example, the interval from -3 to 7 that includes 7 but not -3 is expressed`(-3,7]`. - For infinite intervals, use
`Inf`for ∞ (infinity) and/or`-Inf`for -∞ (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed`[6,Inf)`. - If the set includes more than one interval, they are joined using the union symbol U. For example, the set consisting of all points in (-3,7] together with all points in [-8,-5) is expressed
`[-8,-5)U(-3,7]`

. - If the answer is the empty set, you can specify that by using braces with nothing inside:
`{ }`

- You can use
`R`

as a shorthand for all real numbers. So, it is equivalent to entering`(-Inf, Inf)`

. - You can use set difference notation. So, for all real numbers except 3, you can use
`R-{3}`

or`(-Inf, 3)U(3,Inf)`

(they are the same). Similarly,`[1,10)-{3,4}`

is the same as`[1,3)U(3,4)U(4,10)`

. - WeBWorK will
**not**interpret`[2,4]U[3,5]`as equivalent to`[2,5]`, unless a problem tells you otherwise. All sets should be expressed in their simplest interval notation form, with no overlapping intervals.