﻿

# convergence

/keuhn verr"jeuhns/, n.
1. an act or instance of converging.
2. a convergent state or quality.
3. the degree or point at which lines, objects, etc., converge.
4. Ophthalm. a coordinated turning of the eyes to bear upon a near point.
5. Physics.
a. the contraction of a vector field.
b. a measure of this.
6. Meteorol. a net flow of air into a given region. Cf. divergence (def. 2).
7. Biol. similarity of form or structure caused by environment rather than heredity.
Also, convergency (for defs. 1-3).
[1705-15; CONVERG(ENT) + -ENCE]

* * *

Mathematical property of infinite series, integrals on unbounded regions, and certain sequences of numbers.

An infinite series is convergent if the sum of its terms is finite. The series 12 + 14 + 18 + 116 + 132 + ... sums to 1 and thus is convergent. The harmonic series 1 + 12 + 13 + 14 + 15 + ... does not converge. An integral calculated over an interval of infinite width, called an improper integral, describes a region that is unbounded in at least one direction. If such an integral converges, the unbounded region it describes has finite area. A sequence of numbers converges to a particular number when the difference between successive terms becomes arbitrarily small. The sequence 0.9, 0.99, 0.999, etc., converges to 1.

* * *

in mathematics, property (exhibited by certain infinite series and functions (function)) of approaching a limit more and more closely as an argument (variable) of the function increases or decreases or as the number of terms of the series increases.

For example, the function y = 1/x converges to zero as x increases. Although no finite value of x will cause the value of y to actually become zero, the limiting value of y is zero because y can be made as small as desired by choosing x large enough. The line y = 0 (the x-axis) is called an asymptote of the function.

Similarly, for any value of x between (but not including) −1 and +1, the series 1 + x + x2 +⋯+ xn converges toward the limit 1/(1 − x) as n, the number of terms, increases. The interval −1 < x < 1 is called the range of convergence of the series; for values of x outside this range, the series is said to diverge.

* * *

Universalium. 2010.

Synonyms:

### Look at other dictionaries:

• convergence — [ kɔ̃vɛrʒɑ̃s ] n. f. • 1671; de convergent 1 ♦ Le fait de converger. La convergence de deux lignes. Convergence d un système optique, d une lentille. Rapport de convergence. ⇒ grandissement. Météor. Convergence de deux masses d air. Géol. Zone de …   Encyclopédie Universelle

• Convergence — Con*ver gence, Convergency Con*ver gen*cy, n. [Cf. F. convergence.] 1. The condition or quality of converging; tendency to one point; the occurrence of two or more things coming together. [1913 Webster] 2. (Math.) the approach of an infinite… …   The Collaborative International Dictionary of English

• Convergence — Allgemeine Informationen Genre(s) Rock, Metal, Alternative Metal, Nu Metal Gründung 2001 Website …   Deutsch Wikipedia

• convergence — CONVERGENCE. substant, fémin. Terme de Géométrie. Position réciproque de deux lignes qui vont en s approchant.Convergence. En Dioptrique, c est la disposition des rayons d un corps lumineux, qui vont en s approchant, jusqu à ce qu ils se… …   Dictionnaire de l'Académie Française 1798

• convergence — convergence. См. конвергенция. (Источник: «Англо русский толковый словарь генетических терминов». Арефьев В.А., Лисовенко Л.А., Москва: Изд во ВНИРО, 1995 г.) …   Молекулярная биология и генетика. Толковый словарь.

• convergence — index adjoiner, caucus, center (central position), centralization, coalescence, coalition, collection (accumulation) …   Law dictionary

• convergence — thesis …   Dictionary of sociology

• convergence — (n.) 1713, from CONVERGE (Cf. converge) + ENCE (Cf. ence). Related: Convergent. Convergent evolution was in use among biologists by 1890 …   Etymology dictionary

• convergence — n. pl. convergencies [kən vʉr′jəns] n. [< CONVERGENT] 1. the act, fact, or condition of converging 2. the point at which things converge 3. Biol. the development of similarities in unrelated organisms living in similar environments: Also… …   English World dictionary

• Convergence — Contents 1 Science 1.1 Mathematics 1.2 Natural sciences …   Wikipedia

• Convergence — Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Sur les autres projets Wikimedia : « Convergence », sur le Wiktionnaire (dictionnaire universel) Le terme de convergence est utilisé dans… …   Wikipédia en Français