In mathematics, a limit is a value that a function or sequence approaches as the input or

index approaches some value. Limits are essential to calculus (and mathematical analysis

in general) 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.

In formulas, a limit is usually written as:

lim_n->c f(n) = L

and is read as the limit of f of n as n approaches c equals L. Here lim indicates limit,

and the fact that function f(n) approaches the limit L as n approaches c is represented by

the right arrow (→), as in

f(n) -> L

Suppose f is a real-valued function and c is a real number. Intuitively speaking, the

expression lim_x->c f(x) = L

means that f(x) can be made to be as close to L as desired by making x sufficiently close

to c. In that case, the above equation can be read as the limit of f of x, as x

approaches c, is L