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.


  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. John Wiley & Sons, Inc.. 1972. Last Accessed 6/25/2018. Buy the book

More Information

  • McAdams, David E.. Closed (sets). All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018.

Cite this article as:

McAdams, David E. Closure Property. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/11/2010: Added "References". (McAdams, David E.)
6/7/2008: Corrected spelling. (McAdams, David E.)
3/25/2008: Revised More Information to match current standard. (McAdams, David E.)
7/13/2007: Initial version. (McAdams, David E.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License