Set Notation for Writing Number Intervals | Exercises Algebra

CourtesyofCathyAune,MathematicsInstructor,WOU

SETNOTATION

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Hereisaquicksummaryofthecorrectnotationusedinwritingnumberintervals.

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Therearebasicallytwowaystowritenumberintervals:

(1)IntervalNotationand(2)SetBuilderNotation

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SetBuilderNotationcanbewrittenintwoways.Oneusesbraces{}andtheotherdoesnot.

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InalgebracoursesweusuallyuseIntervalNotation.ButtheshortenedversionofSet

BuilderNotationisalsofine.Usingbracketsisnotrecommended!

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NumbersInterval

NotationSetBuilderSetBuilder

with{}

Allrealnumbers 󰇛∞, ∞󰇜 Allreal

numbers*

Allreal

numbers*

Allrealnumbersbetween‐2and3,

includingneither‐2nor3󰇛2, 3󰇜 2    3 󰇝|2    3󰇞

Allrealnumbersbetween‐2and3,

including‐2butnotincluding3󰇟2, 3󰇜 2    3 󰇝|2    3󰇞

Allrealnumbersbetween‐2and3,

notincluding‐2butincluding3󰇛2, 3󰇠 2    3 󰇝|2    3󰇞

Allrealnumbersbetween‐2and3,

includingboth‐2and3󰇟2, 3󰇠 2    3 󰇝|2    3󰇞

Allrealnumberslessthan‐2butnot

equalto‐2,notincluding‐2󰇛∞, 2󰇜 2 󰇝|2

󰇞

Allrealnumberslessthan‐2,

including‐2󰇛∞, 2󰇠 2 󰇝|2

󰇞

All real numbers greater than 3 but not

equalto3,notincluding3󰇛3, ∞󰇜 3 󰇝|3

󰇞

Allreal numbersgreater thanor equalto

3,including3󰇟3, ∞󰇜 3 󰇝|3

󰇞

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*Notethat“thesetofallrealnumbers”canbewrittenasascriptuppercaseR.In

handwritingweusuallymakeadoublelineintheleftdownstrokeoftheRtoindicatethis.

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Alsopleasenotethat,whilesomemayarguetothecontrary,thenotation∞    ∞is

notconsideredstandard.

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Courtesy of Cathy Aune, Mathematics Instructor, WOU

SET NOTATION

Here is a quick summary of the correct notation used in writing number intervals.

There are basically two ways to write number intervals: (1) Interval Notation and (2) Set Builder Notation

Set Builder Notation can be written in two ways. One uses braces { } and the other does not.

In algebra courses we usually use Interval Notation. But the shortened version of Set Builder Notation is also fine. Using brackets is not recommended!

Numbers

Interval

Notation

Set Builder

with { }

All real numbers ሺെ∞, ∞ሻ All real numbers*

All real numbers*

All real numbers between ‐2 and 3, including neither ‐ 2 nor 3

All real numbers between ‐2 and 3, including ‐ 2 but not including 3

All real numbers between ‐2 and 3, not including ‐ 2 but including 3

All real numbers between ‐2 and 3, including both ‐ 2 and 3

All real numbers less than ‐2 but not equal to ‐2, not including ‐ 2

All real numbers less than ‐2, including ‐ 2

All real numbers greater than 3 but not equal to 3, not including 3

All real numbers greater than or equal to 3, including 3

*Note that “the set of all real numbers” can be written as a script upper case R. In

handwriting we usually make a double line in the left down stroke of the R to indicate this.

Also please note that, while some may argue to the contrary, the notation െ∞ ൏ ݔ൏ ∞ is not considered standard.

Set Notation for Writing Number Intervals, Exercises of Algebra

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SET NOTATION

Numbers

Interval

Notation

Set Builder

Set Builder

with { }

*Note that “the set of all real numbers” can be written as a script upper case R. In