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limit of function

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  • Limit-preserving function (order theory) — In the mathematical area of order theory, one often speaks about functions that preserve certain limits, i.e. certain suprema or infima. Roughly speaking, these functions map the supremum/infimum of a set to the supremum/infimum of the image of… …   Wikipedia

  • Limit of a function — x 1 0.841471 0.1 0.998334 0.01 0.999983 Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1. It is said that the limit of (sin x)/x as x approache …   Wikipedia

  • Limit (mathematics) — This is an overview of the idea of a limit in mathematics. For specific uses of a limit, see limit of a sequence and limit of a function. In mathematics, the concept of a limit is used to describe the value that a function or sequence approaches… …   Wikipedia

  • Limit superior and limit inferior — In mathematics, the limit inferior (also called infimum limit, liminf, inferior limit, lower limit, or inner limit) and limit superior (also called supremum limit, limsup, superior limit, upper limit, or outer limit) of a sequence can be thought… …   Wikipedia

  • limit — limitable, adj. limitableness, n. /lim it/, n. 1. the final, utmost, or furthest boundary or point as to extent, amount, continuance, procedure, etc.: the limit of his experience; the limit of vision. 2. a boundary or bound, as of a country, area …   Universalium

  • Limit of a sequence — n n sin(1/n) 1 0.841471 2 0.958851 ... 10 0.998334 ... 100 0.999983 As the positive integer n becomes larger and larger …   Wikipedia

  • Limit set — In mathematics, especially in the study of dynamical systems, a limit set is the state a dynamical system reaches after an infinite amount of time has passed, by either going forward or backwards in time. Limit sets are important because they can …   Wikipedia

  • Limit point compact — In mathematics, particularly topology, limit point compactness is a certain condition on a topological space which generalizes some features of compactness. In a metric space, limit point compactness, compactness, and sequential compactness are… …   Wikipedia

  • limit — /ˈlɪmət / (say limuht) noun 1. the final or furthest bound or point as to extent, amount, continuance, procedure, etc.: the limit of vision. 2. a boundary or bound, as of a country, tract, district, etc. 3. Obsolete an area or region within… …  

  • Limit (category theory) — In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint… …   Wikipedia

  • Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

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