# Closure Property

Pronunciation: /ˈkloʊ.ʒər ˈprɒp.ər.ti/ Explain

The closure property of real numbers means that for any two real numbers a and b, a + b is a real number and a·b is a real number.[2]

We say that the set of real numbers is closed with respect to addition and multiplication. As a general principle, set closure applies to many other sets and operations.

### References

1. McAdams, David E.. All Math Words Dictionary, closure property. 2nd Classroom edition 20150108-4799968. pg 34. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Niven, Ivan and Zuckerman, Herbert S.. An Introduction to the Theory of Numbers. 3rd edition. pg 194-195. www.archive.org. John Wiley & Sons, Inc.. 1972. Last Accessed 6/25/2018. http://www.archive.org/stream/introductiontoth000497mbp#page/n211/mode/1up. Buy the book

• McAdams, David E.. Closed (sets). allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/c/closed.html.

McAdams, David E. Closure Property. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/closureproperty.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)