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# Big-O Notation

The symbol , pronounced "big-O of ," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function.

In particular, if is an integer variable which tends to infinity and is a continuous variable tending to some limit, if and are positive functions, and if and are arbitrary functions, then it is said that provided that for some constant and all values and .

Note that big-O notation is the inverse of big-omega notation, i.e., that

Additionally, big-O notation is related to little-O notation in that is stronger than and implies .

Asymptotic, Asymptotic Notation, Big-Omega Notation, Big-Theta Notation, Landau Symbols, Little-O Notation, Little-Omega Notation

This entry contributed by Christopher Stover

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## References

Hardy, G. H. and Wright, E. M. "Some Notations." §1.6 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 7-8, 1979.

## Cite this as:

Stover, Christopher. "Big-O Notation." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Big-ONotation.html