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Exercise. Consider the set R. For every x = (x1, 22) E R? and y = (yı, y2) E R², write P1(x, y) =| x – yı |+ | 22 – 2 |, and p2(x, y) = max{| r1 – yı |, | x2 – y2 |}. Prove that (R2, p1) and (R², p2) are metric spaces?

Exercise. Consider the set R. For every x = (x1, 22) E R? and y = (yı, y2) E R², write P1(x, y) =| x – yı |+ | 22 – 2 |, and p2(x, y) = max{| r1 – yı |, | x2 – y2 |}. Prove that (R2, p1) and (R², p2) are metric spaces?

Advanced Engineering Mathematics
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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Exercise. Consider the set R. For every x = (x1, x2) E R2 and y = (y1, Y2) E R², write Pi(x, y) =| a – yi | + | #2 – Y2 |, and P2(x, y) = max{| x1 – Y1 |, | 22 – y2 |}. Prove that (R², p1) and (IR?, P2) are metric spaces?
Transcribed Image Text:Exercise. Consider the set R. For every x = (x1, x2) E R2 and y = (y1, Y2) E R², write Pi(x, y) =| a – yi | + | #2 – Y2 |, and P2(x, y) = max{| x1 – Y1 |, | 22 – y2 |}. Prove that (R², p1) and (IR?, P2) are metric spaces?
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