Lexic.us

Definition of Convergent

1. Adjective. Tending to come together from different directions.

Definition of Convergent

1. a. tending to one point of focus; tending to approach each other; converging.

Definition of Convergent

1. Adjective. That converges or focuses ¹

2. Adjective. (analysis) A sequence $x\_n$ in a metric space with metric ''d'' is convergent to a point $x^*$, denoted as $x\_n\; \backslash rightarrow\; x^*$, if for every $\backslash epsilon\; >\; 0$ there is a natural number ''N'' such that for every $k\; \backslash ge\; N$ : . ¹

3. Noun. (mathematics) the rational number obtained when a continued fraction has been terminated after a finite number of terms ¹

¹ Source: wiktionary.com

Definition of Convergent

1. [adj]

Medical Definition of Convergent

1. Tending toward a common point. (05 Mar 2000)

Lexicographical Neighbors of Convergent

Literary usage of Convergent

Below you will find example usage of this term as found in modern and/or classical literature:

1. Algebra: An Elementary Text-book for the Higher Classes of Secondary Schools by George Chrystal (1893)
"A series which is convergent when all Us terms are taken positively is said to be ABSOLUTELY convergent. It will be seen immediately that there are series ..."

2. The Encyclopaedia Britannica: A Dictionary of Arts, Sciences, and General by Thomas Spencer Baynes (1888)
"It follows that in a convergent serios of positive terms the terms may be grouped together in any manner so as to form a finite number of partial series ..."

3. A Course of Pure Mathematics by Godfrey Harold Hardy (1908)
"When we say that 2wn is 'absolutely convergent' we do not directly assert the ... Extension of Dirichlet's Theorem to absolutely convergent series. ..."

4. The Theory of Functions of a Real Variable and the Theory of Fourier's Series by Ernest William Hobson (1907)
"convergent sequences will now be considered, of which the elements are real numbers ... The definition of a convergent sequence of real numbers is precisely ..."

5. College Algebra by Henry Lewis Rietz, Arthur Robert Crathorne (1919)
"convergent. 17. Divergent. 19. Divergent for all values of x. 20. ... convergent for x > 0, and x < — 1. 23. convergent for x > — 1 and x < — 3. 8. ..."

6. Introduction to the Theory of Analytic Functions by James Harkness, Frank Morley (1898)
"Conditionally convergent Series. We have now to prove a theorem completing the one just proved : namely that when a series is convergent, but not absolutely ..."

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