Limit (mathematics)
Value approached by a mathematical object / From Wikipedia, the free encyclopedia
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In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.[1] Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
In formulas, a limit of a function is usually written as
and is read as "the limit of f of x as x approaches c equals L". This means that the value of the function f can be made arbitrarily close to L, by choosing x sufficiently close to c. Alternatively, the fact that a function f approaches the limit L as x approaches c is sometimes denoted by a right arrow (→ or ), as in
which reads " of tends to as tends to ".
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.