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Let E be any bounded closed set in the complex plane containing an infinite number of points, and let M, be the maximum of |V(x1,..., xn)| as the points X1, ..., X, run through the set E, where V(x1,., xn) = | (x; - (x; – x;) Isi

Let E be any bounded closed set in the complex plane containing an infinite number of points, and let M, be the maximum of |V(x1,..., xn)| as the points X1, ..., X, run through the set E, where V(x1,., xn) = | (x; - (x; – x;) Isi

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 19E: In Exercises 13-24, prove the statements concerning the relation on the set of all integers. 19. If...
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Let E be any bounded closed set in the complex plane containing an infinite number of points, and let M, be the maximum of |V(x1,..., Xn)| as the points X1, ..., X, run through the set E, where = ("x ** * Ix)A Isi<j<n || (x; - x;) (x; – 2/(n(n-1)) is the Vandermonde determinant. Show that M converges das n → ∞.
Transcribed Image Text:Let E be any bounded closed set in the complex plane containing an infinite number of points, and let M, be the maximum of |V(x1,..., Xn)| as the points X1, ..., X, run through the set E, where = ("x ** * Ix)A Isi<j<n || (x; - x;) (x; – 2/(n(n-1)) is the Vandermonde determinant. Show that M converges das n → ∞.
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