Consider the function d: R² x R² → R defined by in{\32 — 22\,1}_if x₁ = otherwise, d(x, y) := for x = (x₁, x₂), y = (₁, 2) (That is, for example for x = (1,2) and y = (2,3), d(x,y) = 1, for x = (1,2) and y = (1, 1.5), d(x, y) = 0.5, and for x = (1,2), y = (1,3), d(x, y) = 1.) 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 x R² → R defined by in{\32 — 22\,1}_if x₁ = otherwise, d(x, y) := for x = (x₁, x₂), y = (₁, 2) (That is, for example for x = (1,2) and y = (2,3), d(x,y) = 1, for x = (1,2) and y = (1, 1.5), d(x, y) = 0.5, and for x = (1,2), y = (1,3), d(x, y) = 1.) 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.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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