Contain (Set)

Pronunciation: /kənˈteɪn/ Explain

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. Merriam-Webster. Last Accessed 8/6/2018.
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 1-3. Thomson, Brooks/Cole. 2005. Buy the book
  3. Potter, Michael. Set Theory and Its Philosophy: A Critical Introduction. pg 31. Oxford University Press, USA. March 11, 2004. Buy the book

Cite this article as:

McAdams, David E. Contain (Set). 6/29/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/20/2010: Added "References". (McAdams, David E.)
7/9/2008: Corrected math error. (McAdams, David E.)
3/25/2008: Changed More Information to current standard. Changed equation from image to text (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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