Let de(x, y) := |x — y|, d₁(x,y) := for x,y E R. Show that (a) d₁ is a metric on R; (b) dẼ and d₁ are not equivalent. |x - y| 1 + x − y|
Let de(x, y) := |x — y|, d₁(x,y) := for x,y E R. Show that (a) d₁ is a metric on R; (b) dẼ and d₁ are not equivalent. |x - y| 1 + x − y|
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Step 1: Define a theorem corresponding to equivalent metric
VIEWStep 2: Show the dE is a metric on R
VIEWStep 3: Show that d1 is a metric on R
VIEWStep 4: Use inequality
VIEWStep 5: Prove that d1 is a metric on R
VIEWStep 6: Use theorem to check dE and d1 are equivalent or not
VIEWStep 7: Use theorem
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