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limit

Value that a function (or sequence) approaches as the argument (or index) approaches some value

ConceptconceptQ177239

Also known as mathematical limit · lim · limiting value

Instance of: concept
Subclass of: mathematical concept
, upper and lower bounds

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a limit is the value that a function approaches as the argument 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.

Overview

All data

39 statements · 15% with external sources · numbers in brackets are citations

Defining formula: \lim_{x \to \infty}f(x) = L :\iff \forall \epsilon > 0 \exists n_0 \forall n>n_0 : |f(n) - L| < \epsilon
TeX string: \lim
Different from: Roman limes
Members / parts: limit from above
limit from below
Facet of: general topology
Field of work: mathematics

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28 identifiers linking limit across the web's reference databases

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15%

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Source last edited August 31, 2026. AIDB refreshes this page daily.

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AIDB. (2026). limit (Q177239). Retrieved from https://aidb.si/e/limit-Q177239