Empty Set
Pronunciation: /ˈɛmp.ti sɛt/ Explain
The empty set is the
unique
set containing no members^{[2]}.
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
 McAdams, David E.. All Math Words Dictionary, empty set. 2nd Classroom edition 201501084799968. pg 69. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Jech, Thomas. Set Theory. 3rd edition. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. Last Accessed 7/9/2018. http://plato.stanford.edu/entries/settheory/. Buy the book
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 4. Thomson, Brooks/Cole. 2005. Last Accessed 7/9/2018. Buy the book
More Information
 McAdams, David E.. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 12/15/2009. https://www.allmathwords.org/en/s/set.html.
Cite this article as:
McAdams, David E. Empty Set. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/e/emptyset.html.
Revision History
4/20/2019: Updated expressions and equations to match new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
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.)