Set Notation

Pronunciation: /sɛt noʊˈteɪ ʃən/ ?

Set notation is a way to tell what is in a set. Usually the set is named with a capital letter like this:

A = {set definition} 1
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 } 2
    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 } 3
    Set C contains all the natural numbers less than 20.


  1. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 2. Thomson, Brooks/Cole, 2005.

More Information

  • Stapel, Elizabeth. Set Notation. Purplemath. 2009-03-12.

Printed Resources

Cite this article as:

Set Notation. 2008-09-06. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2008-09-06: Initial version (McAdams, David.)

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