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.
References
- 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 8/6/2018. http://www.archive.org/stream/introductiontoth000497mbp#page/n211/mode/1up. Buy the book
More Information
- 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.
Cite this article as:
McAdams, David E. Closure Property. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/closureproperty.html.
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.)