In mathematics, **big O notation** is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called **Landau notation**, **Bachmann–Landau notation** (after Edmund Landau and Paul Bachmann), or **asymptotic notation**. In computer science, big O notation is used to classify algorithms by how they respond (*e.g.,* in their processing time or working space requirements) to changes in input size.

Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation. A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function. Associated with big O notation are several related notations, using the symbols *o*, Ω, ω, and Θ, to describe other kinds of bounds on asymptotic growth rates.

Big O notation is also used in many other fields to provide similar estimates.

Read more about Big O Notation: Formal Definition, Example, Usage, Properties, Multiple Variables, Orders of Common Functions, Related Asymptotic Notations, Generalizations and Related Usages, History (Bachmann–Landau, Hardy, and Vinogradov Notations)

### Other articles related to "big o notation, notation, notations":

**Big O Notation**

... With

**Big O notation**, we say that some term "is" (given some function g, where x is one of f's parameters) ... Intuitively this

**notation**groups functions according to their growth respective to some parameter as such, the

**notation**is abusive in two respects It abuses "=", and it invokes terms that are ... It would be appropriate to use the set membership

**notation**and thus write instead of ...

**Big O Notation**- History (Bachmann–Landau, Hardy, and Vinogradov Notations)

... the first volume of which (not yet containing

**big O notation**) was published in 1892 ... Edmund Landau adopted it, and was thus inspired to introduce in 1909 the

**notation**o hence both are now called Landau symbols ... re-introduced the related Omega and Theta

**notations**...

### Famous quotes containing the word big:

“Small children give you headache; *big* children heartache.”

—Russian proverb.