Problem 4. Consider the two following subsets of the real numbers n 2n + 1 S = :n € N CR, T = EN CR. %3D n+1 n+1 Show that sup(S) = 1, sup(T) = 2 and inf(T) = 3/2. Find inf(S). %3D
Problem 4. Consider the two following subsets of the real numbers n 2n + 1 S = :n € N CR, T = EN CR. %3D n+1 n+1 Show that sup(S) = 1, sup(T) = 2 and inf(T) = 3/2. Find inf(S). %3D
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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![**Problem 4.** Consider the two following subsets of the real numbers:
\[
S = \left\{ \frac{n}{n+1} : n \in \mathbb{N} \right\} \subseteq \mathbb{R}, \quad T = \left\{ \frac{2n+1}{n+1} : n \in \mathbb{N} \right\} \subseteq \mathbb{R}.
\]
Show that \(\sup(S) = 1\), \(\sup(T) = 2\), and \(\inf(T) = \frac{3}{2}\). Find \(\inf(S)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05f71249-0159-4369-afdd-b84b5bf21c00%2F72041dc3-562f-4a95-9c3e-0c590a0c0cdb%2Feae8vid_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4.** Consider the two following subsets of the real numbers:
\[
S = \left\{ \frac{n}{n+1} : n \in \mathbb{N} \right\} \subseteq \mathbb{R}, \quad T = \left\{ \frac{2n+1}{n+1} : n \in \mathbb{N} \right\} \subseteq \mathbb{R}.
\]
Show that \(\sup(S) = 1\), \(\sup(T) = 2\), and \(\inf(T) = \frac{3}{2}\). Find \(\inf(S)\).
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