O means “order of” and o means “of lower order than.” If {u n } and {v n } are two sequences such that |u n /v n | < K for sufficiently large n, where K is a constant independent of n, then u n = O(v n ); for example, (2n − 1)/(n2 + 1) = O(1/ n). The symbol O (colloquially called “big O”) also extends to the case of functions of a continuous variable; for example, (x + 1) = O(x). O(1) denotes any function that is defined for all values of x sufficiently large, and which either has a finite limit as x tends to infinity, or at least for all sufficiently large values of x remains less in absolute value than some fixed bound; for example, sin x = O(1).
If limn−>∞u n /v n = 0, then u n = o(v n ) (colloquially called “little o”); for example, log n = o(n), where again the notation extends to functions of a continuous variable; for example, sin x = o(x). Furthermore, u n = o(1) means that u n tends to 0 as n tends to infinity; for example, (log n)/n = o(1). In probability modeling (e.g.,...
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsEditor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this entry
Cite this entry
(2013). O, o Notation. In: Gass, S.I., Fu, M.C. (eds) Encyclopedia of Operations Research and Management Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1153-7_200536
Download citation
DOI: https://doi.org/10.1007/978-1-4419-1153-7_200536
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-1137-7
Online ISBN: 978-1-4419-1153-7
eBook Packages: Business and Economics