Let C([0, 1]) denote the set of all continuous functions f : [0, 1] → R, and let Qn (0, 1] = {r1,r2, r3, - ..} be an enumeration of the set of rational numbers in [0, 1]. For f and g in C([0, 1]), define d(f, g) = 2lf(r:) – g(r:)|. i=0
Let C([0, 1]) denote the set of all continuous functions f : [0, 1] → R, and let Qn (0, 1] = {r1,r2, r3, - ..} be an enumeration of the set of rational numbers in [0, 1]. For f and g in C([0, 1]), define d(f, g) = 2lf(r:) – g(r:)|. i=0
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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Show that d : C([0, 1]) × C([0, 1]) → R is a metric.
![Let C([0, 1]) denote the set of all continuous functions f : [0, 1] → R, and let
Qn (0, 1] = {r1,r2, 13, . ..}
be an enumeration of the set of rational numbers in [0, 1]. For f and g in C([0, 1]), define
d(f, g) = £2*lf(r:) – g(r:)\.
i=0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9edaadac-9631-4602-85ff-74383cddc21e%2Fb1dc22db-2da7-4089-9310-b4012bda233c%2Fz8t2di_processed.png&w=3840&q=75)
Transcribed Image Text:Let C([0, 1]) denote the set of all continuous functions f : [0, 1] → R, and let
Qn (0, 1] = {r1,r2, 13, . ..}
be an enumeration of the set of rational numbers in [0, 1]. For f and g in C([0, 1]), define
d(f, g) = £2*lf(r:) – g(r:)\.
i=0
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