In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation a famous example of such a difference is the remainder term in the prime number theorem. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. The letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity.
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