An Asymptotic Upper Bound-Big Oh

In 1892, P. Bachmann  invented a notation for characterizing the asymptotic behavior of functions. His invention has come to be known as big oh notation:

Definition (Big Oh)     Consider a function f(n) which is non-negative for all integers . We say that ``f(n) is big oh g(n),'' which we write f(n)=O(g(n)), if there exists an integer and a constant c>0 such that for all integers , .

• A Simple Example
• Big Oh Fallacies and Pitfalls
• Properties of Big Oh
• About Polynomials
• About Logarithms
• Tight Big Oh Bounds
• More Big Oh Fallacies and Pitfalls
• Conventions for Writing Big Oh Expressions

Copyright © 1997 by Bruno R. Preiss, P.Eng. All rights reserved.