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Exercise. Consider the set R?. For every r = (x1, x2) E R? and y = (Yı, 42) E R², write P1(x, y) =| x – Yı |+| x2 – y2 |; and P2(x, y) = max{| x1 – yı |; | #2 = 42 |}. Prove that (R², p1) and (R², p2) are metric spaces?

Exercise. Consider the set R?. For every r = (x1, x2) E R? and y = (Yı, 42) E R², write P1(x, y) =| x – Yı |+| x2 – y2 |; and P2(x, y) = max{| x1 – yı |; | #2 = 42 |}. 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 R? and y = (y1, Y2) E R?, write P1(x, y) =| x – y1 | + | x2 – 92 |, and P2(x, y) = max{| *1 – yı |, | *2 – Y2 |}. Prove that (R2, pi) and (IR2, p2) are metric spaces?
Transcribed Image Text:Exercise. Consider the set R?. For every x = (x1, x2) E R? and y = (y1, Y2) E R?, write P1(x, y) =| x – y1 | + | x2 – 92 |, and P2(x, y) = max{| *1 – yı |, | *2 – Y2 |}. Prove that (R2, pi) and (IR2, p2) are metric spaces?
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