Let X be the space of bounded and closed linear segments on the positive part of the real line, so every point in the spa X is a line segment [a, b] C R, a, b > 0. Let dist([a, b], [c, d]) = max{b, d) - min{a, c). Is this a metric on such space X? Consider another function dist([a, b], [c, d]) = max(lc - al, Id-b}. Is this a metric on X? [Hint: You might find the following inequalities useful: max(x+y, u+v} ≤ max(x+max{y, v), u+max{y, v}} ≤ max{x, u} + max{y v}.]
Let X be the space of bounded and closed linear segments on the positive part of the real line, so every point in the spa X is a line segment [a, b] C R, a, b > 0. Let dist([a, b], [c, d]) = max{b, d) - min{a, c). Is this a metric on such space X? Consider another function dist([a, b], [c, d]) = max(lc - al, Id-b}. Is this a metric on X? [Hint: You might find the following inequalities useful: max(x+y, u+v} ≤ max(x+max{y, v), u+max{y, v}} ≤ max{x, u} + max{y v}.]
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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![Let X be the space of bounded and closed linear segments on the positive part of the real line, so every point in the space
X is a line segment [a, b] C R, a, b > 0.
Let dist([a, b], [c, d]) = max{b, d} - min{a, c).
Is this a metric on such space X?
Consider another function dist([a, b], [c, d]) = max{|c-al, d - bl}.
Is this a metric on X?
[Hint: You might find the following inequalities useful: max(x+y, u+v} ≤ max{x+max{y, v}, u+max{y, v}} ≤ max{x, u} + max{y,
v}.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1663884d-336a-4253-8123-d139115018fd%2F51594d69-1e79-4275-8e60-75299ca8aef8%2F5wx2o4nr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X be the space of bounded and closed linear segments on the positive part of the real line, so every point in the space
X is a line segment [a, b] C R, a, b > 0.
Let dist([a, b], [c, d]) = max{b, d} - min{a, c).
Is this a metric on such space X?
Consider another function dist([a, b], [c, d]) = max{|c-al, d - bl}.
Is this a metric on X?
[Hint: You might find the following inequalities useful: max(x+y, u+v} ≤ max{x+max{y, v}, u+max{y, v}} ≤ max{x, u} + max{y,
v}.]
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