Closure Property

Pronunciation: /ˈkloʊ ʒər ˈprɒp ər ti/ ?

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. (Accessed: 2010-01-11).

More Information

  • McAdams, David. Closed (sets). All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-10-29.

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Cite this article as:

Closure Property. 2010-01-11. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2010-01-11: Added "References" (McAdams, David.)
2008-06-07: Corrected spelling (McAdams, David.)
2008-03-25: Revised More Information to match current standard (McAdams, David.)
2007-07-13: Initial version (McAdams, David.)

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