Empty Set

Pronunciation: /ˈɛmp ti sɛt/ ?

The empty set is the unique set containing no members1. The empty set is written or, less often, {}.

Properties of the empty set

A ∪ ∅ = A

Given an arbitrary set A, the union of the empty set and set A is equal to set A.

A ∩ ∅ = ∅ The intersection of an arbitrary set A and the empty set is the empty set.
∅ ⊂ A The empty set is a subset of all other sets.


  1. empty set. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-24). http://www.merriam-webster.com/dictionary/empty set.
  2. Jech, Thomas. Set Theory. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. (Accessed: 2009-12-15). http://plato.stanford.edu/entries/set-theory/.
  3. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 4. Thomson, Brooks/Cole, 2005.

More Information

  • McAdams, David. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-12-15. http://www.allmathwords.org/article.aspx?lang=en&id=Set.

Printed Resources

Cite this article as:

Empty Set. 2009-12-15. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/emptyset.html.


Image Credits

Revision History

2010-01-24: Added "References" (McAdams, David.)
2008-12-17: Expanded 'More Information' (McAdams, David.)
2008-07-14: Added {} as notation, added more information (McAdams, David.)
2008-02-04: Changed equations to graphics to overcome limitations of Internet Explorer (McAdams, David.)
2007-08-01: Initial version (McAdams, David.)

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