Convergence
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In the absence of a more specific context, Convergence denotes the approach toward a definite value, as time goes on; or to a definite point, a common view or opinion, or toward a fixed or equilibrium state.
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Mathematics
In mathematics, convergence describes limiting behaviour, particularly of an infinite sequence or series toward some limit. To assert convergence is to claim the existence of such a limit, which may be itself unknown. For any fixed standard of accuracy, however, you can always be sure to be within that limit, provided you have gone far enough. The following lists more specific usages of this word:
- Convergent series provides a general mathematical definition and a context in which to understand the remaining usages.
- In topology, an infinite sequence of points of a topological space is said to converge to a point x if every neighborhood of x contains all but a finite number of points of the sequence.
- integral test for convergence is a technique used to test infinite series of nonnegative terms for convergence.
- radius of convergence pertains to a domain interval over which a power series converges.
- Uniform convergence pertains to the speed of convergence that is independent of any value in the domain.
- Monotone convergence theorem pertains to any one of several such theorems defined over a monotone sequence of numbers.
- Convergence of random variables pertain to any one of several notions of convergence in probability theory.
- Rate of convergence pertains to the "speed" at which a convergent sequence approaches its limit.
- Absolute convergence pertains to whether the absolute value of the limit of a series or integral is finite.
- Pointwise convergence (no clear introductory statement of context).
- Gromov-Hausdorff convergence pertains to metric spaces and is a generalization of Hausdorff distance.
- Convergence of Fourier series pertains to whether the Fourier series of a periodic function converges. Also known as classic harmonic analysis.
- Dominated convergence theorem pertains to a theorem by Henri Lebesgue.
The opposite of convergence is divergence. Divergence may be some kind of oscillation, unrestricted growth (recognised as the case of an infinite limit), or chaotic behavior. An infinite series that is divergent cannot be used for meaningful computations of its value. Nevertheless, divergent series can be summed formally, as generating functions or asymptotic series, or via some summation method.
Natural sciences
- convergent evolution pertains to organisms not closely related that independently acquire similar characteristics while evolving in separate and sometimes varying ecosystems.
- convergent synthesisis a strategy that aims to improve the efficiency of multi-step chemical synthesis.
- Convergent boundary is a fault boundary defined in the specialty of Geology known as Plate techtonics.
- South Pacific convergence zone in Meteorology is a belt of low atmospheric pressure extending from the west Pacific warm pool south-eastwards towards French Polynesia.
- Intertropical convergence zone in Meteorology is a belt of low atmospheric pressure girdling the globe at the equator.
Computing and technology
- Convergence (evolutionary computing) is a means of modelling the tendency for genetic characteristics of populations to stabilize over time.
- Premature convergence is an anomaly in Evolutionary computation in which the population evolved to some stable yet sub-optimal state.
- Converge PL is a dynamic object-oriented programming language with compile-time meta-programming facilities.
- Convergent Technologies is a company that designed an operating system for the early Intel and Motorola chipsets.
- Technological convergence refers to the trend for some set of technologies initially having distinct functionalities to evolve to having those that overlap.
- Convergence in the media occurs when multiple products come together to form one product with the advantages of all of them.
Social sciences
- Language convergence pertains to the blending of two languages that are perceived as having equal social status. Opposite of Non-convergent discourse.
- Non-convergent discourse pertains to the persistence of asymmetric or bilingual discourse in natural languages.
- Catch-up effect is otherwise known as the Theory of convergence in economic theory.
- In the context of bargaining, Convergence pertains to a behavior in which the price offered by a buyer may increase while the price acceptable to a seller may decrease until both prices approach equality, in which case they are said to converge.
- Convergence criteria are requirements specified by the European Union that stipulate the membership qualifications each state must fulfill.
Politics
- Convergence (Mexico) is a political party in Mexico that was previously known as Convergence for Democracy.
- Democratic Convergence Party either of two unrelated political parties that includes either Democratic Convergence Party (Cape Verde) Islands or Democratic Convergence Party-Reflection Group in Portugal.
- Convergence and Unity a coalition of the the two political parties Democratic Convergence of Catalonia and the Democratic Union of Catalonia in Catalonia Spain.
- Democratic Convergence of Cataloniais a Catalan nationalist political party in Catalonia Spain.
- Convergence for Social Democracy is an opposition political party in Equatorial Guinea.
- Anti-Capitalist Convergence a group of umbrella (political) organizations that coordinate social justice, anarchist, and environmentalist activities.
Science fiction and popular culture
- Convergence (goth festival) refers to an annual convention in which goths meet each other in 'real life' rather than online, as is customarily done.
- CONvergence (convention) is a speculative fiction convention in Minnesota.
- Harmonic Convergence was a new age spiritual event that took place on one day in 1987 observed worldwide.
- Converge (band) was a forerunner of the mathcore genre.
- Convergence is an album by James Murphy.
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