View source for Limit (mathematics)

In [[mathematics]], a '''limit''' is the value that a [[Function (mathematics)|function]] or [[sequence]] "approaches" as the input or index approaches some value.

== Description ==

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.

== See also ==

* [[Asymptotic analysis]]: a method of describing limiting behavior
** [[Big O notation]]: used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity
* [[Convergent matrix]]
* [[Cauchy sequence]]
** [[Complete metric space]]
* [[Function (mathematics)]]
* [[Limit of a function]]
** [[One-sided limit]]: either of the two limits of functions of a real variable x, as x approaches a point from above or below
** [[List of limits]]: list of limits for common functions
** [[Squeeze theorem]]: finds a limit of a function via comparison with two other functions
* [[Modes of convergence]]
** An [[annotated index]]
* [[Convergence of random variables]]
* [[Banach limit]] defined on the Banach space that extends the usual limits.
* [[Limit in category theory]]
** [[Direct limit]]
** [[Inverse limit]]
* [[Rate of convergence]]: the rate at which a convergent sequence approaches its limit

== External links ==

* [https://en.wikipedia.org/wiki/Limit_(mathematics) Limit (mathematics)] @ Wikipedia


[[Category:Mathematics]]