Tag: limit

In mathematics, a limit is the 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, limit is usually abbreviated as lim as in lim(an) = a, and the fact of approaching a limit is represented by the right arrow (→) as in an → a.
Suppose f(x) is a real-valued function and c is a real number. The expression
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”.
Augustin-Louis Cauchy in 1821, followed by Karl Weierstrass, formalized the definition of the limit of a function as the above definition,…