Show that for all f and g in C([0,1]), d(f,g) is a (finite) real number. Let C([0, 1]) denote the set of all continuous functions f : [0, 1] → R, and letQn (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]), defined(f, g) = £2*lf(r:) – g(r:)\.i=0

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Let C([0, 1]) denote the set of all continuous functions f : [0, 1] → R, and let Qn (0, 1] = {r1,"2;, "3, . ..} 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,"2;, "3, . ..} 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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Question

Show that for all f and g in C([0,1]), d(f,g) is a (finite) real number.

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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