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Consider the function d: R² × R² → R$ defined by [min{\32 - x₂, 1} if x₁ = y₁ 1 otherwise, d(x, y) = for x = (x₁, x2), y = (y₁, y2) (That is, for example for x = (1, 2) and y = (2,3), d(x, y) y = (1, 1.5), d(x, y) = 0.5, and for x = = (1,2), y = (1,3), d(x, y) = 1.) = 1, for x = (1, 2) and Is this a well-define metric on R2? Argue for each condition of a metric if it is satisfied and provide a justification or counterexample.

Consider the function d: R² × R² → R$ defined by [min{\32 - x₂, 1} if x₁ = y₁ 1 otherwise, d(x, y) = for x = (x₁, x2), y = (y₁, y2) (That is, for example for x = (1, 2) and y = (2,3), d(x, y) y = (1, 1.5), d(x, y) = 0.5, and for x = = (1,2), y = (1,3), d(x, y) = 1.) = 1, for x = (1, 2) and Is this a well-define metric on R2? Argue for each condition of a metric if it is satisfied and provide a justification or counterexample.

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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Consider the function d: R² × R² → R defined by {} d(x, y) = min{|y2x₂, 1} if x₁ = y₁ otherwise, 1 for x = (x₁, x₂), Y = (Y₁, Y2) (That is, for example for x = (1,2) and y = (2,3), d(x, y) = y = (1, 1.5), d(x, y) = 0.5, and for x = (1,2), y = (1,3), d(x, y) = 1.) = 1, for x = (1, 2) and Is this a well-define metric on R2? Argue for each condition of a metric if it is satisfied and provide a justification or counterexample.
Transcribed Image Text:Consider the function d: R² × R² → R defined by {} d(x, y) = min{|y2x₂, 1} if x₁ = y₁ otherwise, 1 for x = (x₁, x₂), Y = (Y₁, Y2) (That is, for example for x = (1,2) and y = (2,3), d(x, y) = y = (1, 1.5), d(x, y) = 0.5, and for x = (1,2), y = (1,3), d(x, y) = 1.) = 1, for x = (1, 2) and Is this a well-define metric on R2? Argue for each condition of a metric if it is satisfied and provide a justification or counterexample.
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