please see the picture. Let S be a subset of R. We say that S is dense in R, if(D) for any > 0 and any x ∈ R, there is s ∈ S − {x} such that |x − s| ≤ .(i) Write down the negation of (D) as a complete sentence.(ii) Using the result of Problem 1, show that Q is dense in R.(iii) Show that Z is not dense in R. (In other words, show that Z satisfies the negation of (D)). 22. Let S be a subset of R. We say that S is dense in R, if(D) for any € >0 and any x R, there is s E S- {x} such that |xs| ≤ €.(i) Write down the negation of (D) as a complete sentence.(ii) Using the result of Problem 1, show that Q is dense in R.(iii) Show that Z is not dense in R. (In other words, show that Z satisfies the negation of (D)).

Answered: Image /qna-images/answer/22a27eda-5961-4567-b795-4f589a2e41fe.jpg

2. Let S be a subset of R. We say that S is dense in R, if (D) for any € > 0 and any x R, there is sS- {x} such that |x-s| ≤ €. (i) Write down the negation of (D) as a complete sentence. (ii) Using the result of Problem 1, show that Q is dense in R. (iii) Show that Z is not dense in R. (In other words, show that Z satisfies the negation of (D)).

2. Let S be a subset of R. We say that S is dense in R, if (D) for any € > 0 and any x R, there is sS- {x} such that |x-s| ≤ €. (i) Write down the negation of (D) as a complete sentence. (ii) Using the result of Problem 1, show that Q is dense in R. (iii) Show that Z is not dense in R. (In other words, show that Z satisfies the negation of (D)).

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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