Suppose C 1 , C 2 , C 3 , . . . is a nondecreasing sequence
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Suppose C1, C2, C3, . . . is a nondecreasing sequence of sets, i.e., Ck ⊂ Ck+1, for k = 1, 2, 3, . . . . Then limk→∞ Ck is defined as the union C1 ∪C2 ∪C3∪· · ·. Find limk→∞ Ck if
(a) Ck = {x : 1/k ≤ x ≤ 3 − 1/k}, k = 1, 2, 3, . . . .
(b) Ck = {(x, y) : 1/k ≤ x2 + y2 ≤ 4 − 1/k}, k = 1, 2, 3, . . . .
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Related Book For
Introduction To Mathematical Statistics
ISBN: 9780321794710
7th Edition
Authors: Robert V., Joseph W. McKean, Allen T. Craig
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