Contain (Set)

Pronunciation: /kənˈteɪn/ ?

A set contains another set if all the members of the contained set are also members of the containing set.[1] If set A contains set B we can also say the set B is a subset of set A, and write B ⊂ A.

Example 1

Diagram showing set A as a large circle and set B as a small circle all the way inside of the circle for A.
Figure 1: Set A contains set B.

Example 2

The set of real numbers contains the set of integers because every integer is also a real number.


  1. contain. Encyclopedia Britannica. (Accessed: 2010-01-05).
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 1-3. Thomson, Brooks/Cole, 2005.
  3. Potter, Michael. Set Theory and Its Philosophy: A Critical Introduction , pg 31. Oxford University Press, USA, March 11, 2004.

More Information

  • McAdams, David. Contain (Geometry). All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-01-20.

Printed Resources

Cite this article as:

Contain (Set). 2010-01-05. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2010-01-20: Added "References" (McAdams, David.)
2008-07-09: Corrected math error (McAdams, David.)
2008-03-25: Changed More Information to current standard. Changed equation from image to text (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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