# Limits & Derivatives

In mathematics, a **limit** is the value that a function or sequence "approaches" as the input or index approaches some value.^{[1]} 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 denoted "lim" as in lim_{n → c}(*a*_{n}) = *L*, and the fact of approaching a limit is represented by the right arrow (→) as in *a*_{n} → *L*.