SETNOTATION
Hereisaquicksummaryofthecorrectnotationusedinwritingnumberintervals.
Therearebasicallytwowaystowritenumberintervals:
(1)IntervalNotationand(2)SetBuilderNotation
SetBuilderNotationcanbewrittenintwoways.Oneusesbraces{}andtheotherdoesnot.
InalgebracoursesweusuallyuseIntervalNotation.ButtheshortenedversionofSet
BuilderNotationisalsofine.Usingbracketsisnotrecommended!
Numbers
Interval
Notation
SetBuilder
SetBuilder
with{}
Allreal
numbers*
Allreal
numbers*
Allrealnumbers
∞, ∞ Allrealnumbersbetween‐2and3,
includingneither‐2nor3
2, 3 2
3
| 2
3
Allrealnumbersbetween‐2and3,
including‐2butnotincluding3
2, 3 2
3
| 2
3
Allrealnumbersbetween‐2and3,
notincluding‐2butincluding3
2, 3 2
3
| 2
3
Allrealnumbersbetween‐2and3,
includingboth‐2and3
2, 3 2
3
| 2
3
Allrealnumberslessthan‐2butnot
equalto‐2,notincluding‐2
∞, 2 2
|
2
Allrealnumberslessthan‐2,
including‐2
∞, 2 2
|
2
All real numbers greater than 3 but not
equalto3,notincluding3
3, ∞ 3
|
3
Allrealnumbersgreaterthanorequalto
3,including3
3, ∞ 3
|
3
*Note that “the set of all real numbers” can be written as a script upper case R. In
handwritingweusuallymakeadoublelineintheleftdownstrokeoftheRtoindicatethis.
Alsopleasenotethat,whilesomemayarguetothecontrary,thenotation ∞
∞is
notconsideredstandard.
Courtesy of Cathy Aune, Mathematics Instructor, WOU