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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. Limits are very important in calculus (and mathematical analysis in general). They are used to define continuity, derivatives, and integrals.
In formulas, limit is usually abbreviated as lim as in lim(an) = a. If an expression is approaching a limit, it is represented by the right arrow (→) as in an → a.
- Limit of a sequence
- Cauchy sequence
- Limit of a function
- 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