In mathematics, a limit is the value that a function or sequence “approaches” as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit is usually written as : and is read as “the limit of f of n as n approaches c equals L”. Here “lim” indicates limit, and the fact that function f(n) approaches the limit L as n approaches c is represented by the right arrow (→), as in :