Let $${\displaystyle \ f\ ,}$$ the function to be estimated, be a real or complex valued function, and let $${\displaystyle \ g\ ,}$$ the comparison function, be a real valued function. Let both functions be defined on some See more

Big O notation has two main areas of application:
• In mathematics, it is commonly used to describe how closely … See more

Big O (and little o, Ω, etc.) can also be used with multiple variables. To define big O formally for multiple variables, suppose $${\displaystyle f}$$ See more

Big O is widely used in computer science. Together with some other related notations, it forms the family of Bachmann–Landau notations.
Little-o notation See more

In typical usage the O notation is asymptotical, that is, it refers to very large x. In this setting, the contribution of the terms that grow "most quickly" will eventually make the … See more

If the function f can be written as a finite sum of other functions, then the fastest growing one determines the order of f(n). For example,
In particular, if a … See more

Equals sign
The statement "  f(x)   is   O[ g(x) ]  " as defined above is usually written as   f(x) = O[ g(x) ]  . Some consider this to be an abuse of notation, … See more