#4. Prove thata rectangle R = [a1, bil x ...x [an, bn] C R" is closed. *5. Prove that the closed ball B (a, r) {x e R" : ||x - a|| < r} C R" is closed. F6. Given a sequence {xk} of points in R", a subsequence is formed by taking where k1 < k2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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I need help for number 5.

There are some parts in this section that I don't understand. Please give me as much detail as possible for number 5. Thank you very much!

#4. Prove thata rectangle R = [a1, bil x ...x [an, bn] C R" is closed.
*5. Prove that the closed ball B (a, r)
{x e R" : ||x - a|| < r} C R" is closed.
F6. Given a sequence {xk} of points in R", a subsequence is formed by taking
where k1 < k2 <k3
Transcribed Image Text:#4. Prove thata rectangle R = [a1, bil x ...x [an, bn] C R" is closed. *5. Prove that the closed ball B (a, r) {x e R" : ||x - a|| < r} C R" is closed. F6. Given a sequence {xk} of points in R", a subsequence is formed by taking where k1 < k2 <k3
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