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Limit (mathematics)
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This is an overview of the idea of a limit in mathematics. For specific uses of a limit, see limit of a sequence and limit of a function.
In mathematics, a limit is the value that a function or sequence "approaches" or comes close to as the argument or index comes close to some value.^{[1]} Limits are very important in calculus (and mathematical analysis in general). They are used to define continuity, derivatives, and integrals.
The concept of a limit of a sequence can be generalised to the idea of a limit of a topological net. It is closely related to limit and direct limit in category theory.
In formulas, limit is usually abbreviated as lim as in lim(a_{n}) = a. If an expression is approaching a limit, it is represented by the right arrow (→) as in a_{n} → a.
Other pages
 Limit of a sequence
 Rate of convergence: the rate at which a convergent sequence approaches its limit
 Cauchy sequence
 Limit of a function
 Onesided limit: a real variable x has two limits, as x approaches a point from above or below. This refers to one of those limits.
 List of limits: list of limits for common functions
 Squeeze theorem: finds a limit of a function by comparing it with that of two other functions.
 Banach limit defined on the Banach space that extends the usual limits.
 Limit in category theory
 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
Notes
 ↑ Stewart, James (2008). Calculus: Early Transcendentals (6th ed.). Brooks/Cole. .
Other websites
 Weisstein, Eric W., "Limit" from MathWorld.
 Mathwords: Limit
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