Limit (mathematics)

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.

Description

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.

See also

[[Function (mathematics)

• Rate of convergence: the rate at which a convergent sequence approaches its limit
• Cauchy sequence
  • Complete metric space
• Limit of a function
  • One-sided limit: either of the two limits of functions of a real variable x, as x approaches a point from above or below
  • List of limits: list of limits for common functions
  • Squeeze theorem: finds a limit of a function via comparison with two other functions
• Modes of convergence
  • An annotated index
• Convergence of random variables
• Banach limit defined on the Banach space that extends the usual limits.
• Limit in category theory
  • Direct limit
  • Inverse limit
• 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

External links

• Limit (mathematics) @ Wikipedia