Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are essential to calculus and mathematical analysis, 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. The limit inferior and limit superior provide generalizations of the concept of a limit which are particularly relevant when the limit at a point may not exist. Read by Dylan1496. Recorded June 6, 2021; the article may have changed since. The article as it stood when recorded: https://en.wikipedia.org/w/index.php?oldid=1026996783 Article today: https://en.wikipedia.org/wiki/Limit_(mathematics) Original recording: https://commons.wikimedia.org/wiki/File:En-Limit_Mathematics-article.ogg License: CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0). This episode is a format-shifted (MP3) copy redistributed under the same license. This show is an independent community project, not affiliated with or endorsed by the Wikimedia Foundation.