limit

In mathematics, a value approached by a variable. The variable may be the sum of a number of terms of a sequence, eg if as n becomes large (ie n ? ?), S approaches the value 2. Or the variable y may be dependent on another variable x, and may approach a limit as x approaches a given value, eg if y = 2 + 1/x, y approaches the value 2 as x becomes large. The idea of a limit is fundamental to calculus and other branches of mathematics. The limit, L, of a function f(x) as x approaches a value x₀ is defined, when it exists, by the rule that for every ?>0, there is a ?>0 such that implies that . This way to define limits was successfully introduced into mathematics in the 1820s by French mathematician Augustin Louis Cauchy (1789–1857) as part of the first adequate attempt to rigorize the calculus.

A limit can be:

Limit (mathematics), including: Limit of a function Limit of a sequence Limit superior and limit inferior Limit of a net Limit point Limit (category theory) A constraint (mathematical, physical, economical, legal, etc.) in the form of an inequality, such as: Chandrasekhar limit Greisen-Zatsepin-Kuzmin limit Budget constraint Speed limit Age of consent An extreme value or boundary, such as: High frequency limit Limit (music) in just intonation In the BDSM world, limits refer to activities that a partner feels strongly about, and to which special attention must be paid. Limit Break are powerful techniques in the Final Fantasy series

This disambiguation page lists articles associated with the same title.