{ne N} is neither open nor closed; 1 Let S = {:n € N} and take xo € S. To show that S is not open, prove that, for all € > 0, D (xo, €) S- Explain why? To show that for all e > 0, D (xo, e) S, you may consider the following steps: . Observe that co= 1, for some N € N. • Notice that D (x0, €) = ( − €, ½ + €) - Explain why? • Use the fact that an open interval in R is not countable to show that D (xo, e) S. What is the cardinality of S'? To show that S is not closed, prove that S = R\S is not open. To show that Se is not open, prove that, for all € > 0, D (0, €) Sc - Why is this sufficient? Please explain. • Notice that D (0, €) Sc iff D (0, €) • Observe that 0 € Sc and take € > 0. there is NE N, such that 0 << €. • Show that there is x E D (0, e) S. What can you take for x? SØ - Explain why? Which property of real numbers will you use to show that

{ne N} is neither open nor closed; 1 Let S = {:n € N} and take xo € S. To show that S is not open, prove that, for all € > 0, D (xo, €) S- Explain why? To show that for all e > 0, D (xo, e) S, you may consider the following steps: . Observe that co= 1, for some N € N. • Notice that D (x0, €) = ( − €, ½ + €) - Explain why? • Use the fact that an open interval in R is not countable to show that D (xo, e) S. What is the cardinality of S'? To show that S is not closed, prove that S = R\S is not open. To show that Se is not open, prove that, for all € > 0, D (0, €) Sc - Why is this sufficient? Please explain. • Notice that D (0, €) Sc iff D (0, €) • Observe that 0 € Sc and take € > 0. there is NE N, such that 0 << €. • Show that there is x E D (0, e) S. What can you take for x? SØ - Explain why? Which property of real numbers will you use to show that

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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For the following questions, THERE IS NO NEED FOR EXPLANATION. PLEASE PROVIDE JUST THE ANSWER THANK YOU. Please DO NOT waste time on writing things to explain. Please answer in 30 mintues or else I will write a bad review. If you follow my rules and answer in less than 30 mintues then I will write a very long and wonderful review about you. ANSWER the questions correlty and please answer all the questions with what it regards in saying exactly. Ive read the guide lines and honor code that i can have up to Submit only one question at a time under the appropriate subject. A question can have up to 3 subparts (i.e. part a, b, and c). If you dont belive me here is the link of barthleby saying exactly that thanks: https://bartleby.zendesk.com/hc/en-us/articles/360017462394-How-can-I-ensure-my-questions-get-answered-as-quickly-as-possible-
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For the following questions, THERE IS NO NEED FOR EXPLANATION. PLEASE PROVIDE JUST THE ANSWER THANK YOU. Please DO NOT waste time on writing things to explain. Please answer in 30 mintues or else I will write a bad review. If you follow my rules and answer in less than 30 mintues then I will write a very long and wonderful review about you. ANSWER the questions correlty and please answer all the questions with what it regards in saying exactly. Ive read the guide lines and honor code that i can have up to Submit only one question at a time under the appropriate subject. A question can have up to 3 subparts (i.e. part a, b, and c). If you dont belive me here is the link of barthleby saying exactly that thanks: https://bartleby.zendesk.com/hc/en-us/articles/360017462394-How-can-I-ensure-my-questions-get-answered-as-quickly-as-possible-
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