Empty Set
Pronunciation: /ˈɛmp ti sɛt/ ?
The empty set is the
unique
set containing no members^{1}.
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.

References
 empty set. merriamwebster.com. Encyclopedia Britannica. (Accessed: 20100124). http://www.merriamwebster.com/dictionary/empty set.
 Jech, Thomas. Set Theory. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. (Accessed: 20091215). http://plato.stanford.edu/entries/settheory/.
 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. 20091215. http://www.allmathwords.org/article.aspx?lang=en&id=Set.
Printed Resources
Cite this article as:
Empty Set. 20091215. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/emptyset.html.
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Revision History
20100124: Added "References" (
McAdams, David.)
20081217: Expanded 'More Information' (
McAdams, David.)
20080714: Added {} as notation, added more information (
McAdams, David.)
20080204: Changed equations to graphics to overcome limitations of Internet Explorer (
McAdams, David.)
20070801: Initial version (
McAdams, David.)