# Problem StatementConsider 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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Answered: limit points?

Math

Advanced Math

limit points?

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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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

# 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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