Exercise 1.4.6 a. Show that every closed interval [a, b] is the intersection of countably many open intervals. b. Show that every open interval (a, b) is a countable union of closed intervals. c. Show that an intersection of a possibly infinite family of bounded closed intervals, n[ax, bx], is either empty, a single point, or a bounded closed interval. ΧΕΙ
Exercise 1.4.6 a. Show that every closed interval [a, b] is the intersection of countably many open intervals. b. Show that every open interval (a, b) is a countable union of closed intervals. c. Show that an intersection of a possibly infinite family of bounded closed intervals, n[ax, bx], is either empty, a single point, or a bounded closed interval. ΧΕΙ
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please do the first exercise... parts a through c, with detailed explanations
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Exercise 1.4.6
(a) To Show: Every closed interval is the intersection of countable many open intervals.
(b) To Show: Every open interval is a countable union of closed intervals.
(c) To Show: An intersection of a possibly infinite family of bounded closed intervals, , is either empty, a single point, or a bounded closed interval.
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