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.[1]

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. 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 8/6/2018. 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. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

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.)

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