# 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

1. McAdams, David E.. All Math Words Dictionary, empty set. 2nd Classroom edition 20150108-4799968. pg 69. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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/set-theory/. Buy the book
3. 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

• 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.

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.)