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In Problems 1 through 8 find l.u.b. S and g.l.b. S. State whether or not these numbers are in S. 1. S= {x: 00} 5. S= {S: S, (1/2¹), n= 1,2,...} 6. S {S: S1 + ((-1)/i!), n = 1,2, ...}

In Problems 1 through 8 find l.u.b. S and g.l.b. S. State whether or not these numbers are in S. 1. S= {x: 00} 5. S= {S: S, (1/2¹), n= 1,2,...} 6. S {S: S1 + ((-1)/i!), n = 1,2, ...}

Advanced Engineering Mathematics
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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**Problems** In Problems 1 through 8, find the least upper bound (l.u.b.) and the greatest lower bound (g.l.b.) of set \( S \). State whether or not these numbers are in \( S \). 1. \( S = \{x: 0 < x \leq 3\} \) 2. \( S = \{x: x^2 - 3 < 0\} \) 3. \( S = \{x: x^2 - 2x - 3 < 0\} \) 4. \( S = \{y: y = x/(x + 1), x \geq 0\} \) 5. \( S = \{s_n: s_n = \sum_{i=1}^{n}(1/2^i), n = 1, 2, \ldots\}\) 6. \( S = \{s_n: s_n = 1 + \sum_{i=1}^{n}((−1)^i/i!), n = 1, 2, \ldots\}\) 7. \( S = \{x: 0 < x < 5, \cos x = 0\} \)
Transcribed Image Text:**Problems** In Problems 1 through 8, find the least upper bound (l.u.b.) and the greatest lower bound (g.l.b.) of set \( S \). State whether or not these numbers are in \( S \). 1. \( S = \{x: 0 < x \leq 3\} \) 2. \( S = \{x: x^2 - 3 < 0\} \) 3. \( S = \{x: x^2 - 2x - 3 < 0\} \) 4. \( S = \{y: y = x/(x + 1), x \geq 0\} \) 5. \( S = \{s_n: s_n = \sum_{i=1}^{n}(1/2^i), n = 1, 2, \ldots\}\) 6. \( S = \{s_n: s_n = 1 + \sum_{i=1}^{n}((−1)^i/i!), n = 1, 2, \ldots\}\) 7. \( S = \{x: 0 < x < 5, \cos x = 0\} \)
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