Consider a finite set A = {a1, a2, . . . , aN}. To show that A has measure zero, let > 0 be arbitrary. For each 1 ≤ n ≤ N, construct the interval Gn = (an - 2NF, an +2N.Clearly, A is contained in the union of these intervals, and= €.Nn=1n=1

As per the question we are given a finite set A = {a1, a2, . . . , aN}. And we have to show that A…

Answered: Gn = (an - 2N F, an + 2N. Clearly, A is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider a finite set A = {a1, a2, . . . , aN}. To show that A has measure zero, let > 0 be arbitrary. For each 1 ≤ n ≤ N, construct the interval

Gn = (an - 2N
F, an +
2N.
Clearly, A is contained in the union of these intervals, and
= €.
N
n=1
n=1

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Introduction

As per the question we are given a finite set A = {a₁, a₂, . . . , a_N}.

And we have to show that A has measure zero, by assuming an arbitrary ε > 0 and for each 1 ≤ n ≤ N, the union of the sequence of intervals G_n contains the set A whose measure tends to zero.

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