Set Notation

Pronunciation: /sɛt noʊˈteɪ.ʃən/ Explain

Set notation is a way to state what is in a set. Usually the set is named with a capital letter like this: A = {set definition} The definition of the set is inside of curly brackets: {}. There are two styles of set definition that can be in curly brackets.

  • List: If a set has just a few elements, the set can be defined by listing all of the elements: B = { book, pencil, eraser } In this definition, the set B has three elements: book, pencil, and eraser.
  • Rule: A set can be defined by a rule. While this rule can simply be a sentence such as {The set of all rocks in my yard}, math symbols are typically used: C = { x | x, x < 20 } Set C contains all the natural numbers less than 20.


  1. McAdams, David E.. All Math Words Dictionary, set notation. 2nd Classroom edition 20150108-4799968. pg 163. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 2. Thomson, Brooks/Cole. 2005. Buy the book

More Information

  • Stapel, Elizabeth. Set Notation. Purplemath. 3/12/2009.

Cite this article as:

McAdams, David E. Set Notation. 5/7/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

5/7/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/6/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
9/6/2008: Initial version. (McAdams, David E.)

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