# Big O Notation

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.

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

Abuse Of Notation - Examples - 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 ...

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