Empty Set

Pronunciation: /ˈɛmp ti sɛt/ Explain

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. Jech, Thomas. Set Theory. 3rd edition. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. Last Accessed 8/6/2018. http://plato.stanford.edu/entries/set-theory/. Buy the book
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 4. Thomson, Brooks/Cole. 2005. Buy the book

More Information

  • McAdams, David E.. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 12/15/2009. http://www.allmathwords.org/en/s/set.html.

Cite this article as:

McAdams, David E. Empty Set. 7/10/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/emptyset.html.

Revision History

7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/24/2010: Added "References". (McAdams, David E.)
12/17/2008: Expanded 'More Information'. (McAdams, David E.)
7/14/2008: Added {} as notation, added more information. (McAdams, David E.)
2/4/2008: Changed equations to graphics to overcome limitations of Internet Explorer. (McAdams, David E.)
8/1/2007: Initial version. (McAdams, David E.)

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