We are creating the world's most trusted encyclopedia and knowledge base. Once you join us and log in, you'll be able to edit this page instantly!

From Citizendium, the Citizens' Compendium

The big O notation is a mathematical notation to express various bounds concerning asymptotic behaviour of functions. It is often used in particular applications in physics, computer science, engineering and other applied sciences. For example, a typical context use in computer science is to express the complexity of algorithms.

More formally, if f and g are real valued functions of the real variable t then the notation f(t) = O(g(t)) indicates that there exist a real number T and a constant C such that for all t > T.

Similarly, if a_n and b_n are two numerical sequences then a_n = O(b_n) means that for all n big enough.

The big O notation is also often used to indicate that the absolute value of a real valued function around some neighbourhood of a point is upper bounded by a constant multiple of the absolute value of another function, in that neigbourhood. For example, for a real number t₀ the notation f(t) = O(g(t − t₀)), where g(t) is a function which is continuous at t = 0 with g(0) = 0, denotes that there exists a real positive constant C such that on some neighbourhood N of t₀.