Calculate ∪ ∞ n = 1 An and ∩ ∞ n=1 Anywhere for each n ∈ N the set Anis defined as: (i) An= {0, 1, 2, 3, ··· , 2n} (ii) An= {x ∈R|x > n} (iii) An= {x ∈R| 1/n< x < √2 + 1/n}
Calculate ∪ ∞ n = 1 An and ∩ ∞ n=1 Anywhere for each n ∈ N the set Anis defined as: (i) An= {0, 1, 2, 3, ··· , 2n} (ii) An= {x ∈R|x > n} (iii) An= {x ∈R| 1/n< x < √2 + 1/n}
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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Calculate ∪ ∞ n = 1 An and ∩ ∞ n=1 Anywhere for each n ∈ N the set Anis defined as:
(i) An= {0, 1, 2, 3, ··· , 2n}
(ii) An= {x ∈R|x > n}
(iii) An= {x ∈R| 1/n< x < √2 + 1/n}
(iv) An= {x ∈R|−n < x < 1/n}
(v) An= {x ∈Q|√2 − 1/n≤ x ≤ √2 + 1/n}
(vi) An= {n −1, n, n + 1}
(vii) An= [−1, 3 + 1/n] ∪[5, (5n + 1)/n )
(viii) An= (−1/n, 1] ∪(2, (3n −1)/n ]
(ix) An= [0, (n + 1) / (n + 2) ] ∪ [7, (7n + 1) / n )
(x) An= [ 3/n , (5n + 2) / n ) ∪ {10 + n}
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