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limit points?

limit points?

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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# Problem Statement Consider the sets \( A = \{(-1)^n + \frac{1}{n} : n \in \mathbb{N}\} \) and \( B = \{r \in \mathbb{Q} : 0 < r < 1\} \). For each set, answer the following (you do **not** need to prove your responses): ### (a) What are the limit points? ### (b) Is the set open? ### (c) Is the set closed? ### (d) Does the set contain any isolated points? ### (e) Find the closure of the set. --- *Note: The problem requires the analysis of the sets \( A \) and \( B \) with respect to their topological properties such as limit points, openness, closedness, isolated points, and closure.*
Transcribed Image Text:# Problem Statement Consider the sets \( A = \{(-1)^n + \frac{1}{n} : n \in \mathbb{N}\} \) and \( B = \{r \in \mathbb{Q} : 0 < r < 1\} \). For each set, answer the following (you do **not** need to prove your responses): ### (a) What are the limit points? ### (b) Is the set open? ### (c) Is the set closed? ### (d) Does the set contain any isolated points? ### (e) Find the closure of the set. --- *Note: The problem requires the analysis of the sets \( A \) and \( B \) with respect to their topological properties such as limit points, openness, closedness, isolated points, and closure.*
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