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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 limn → c(an) = L, and the fact of approaching a limit is represented by the right arrow (→) as in an → L.

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