Let a = (a, az); b = (b, ,b2) € R?, define the function %3D %3D d: R? x R? ---> R by d=(a, b) = |b,-a, I + do(az, b2), where do denotes the discrete metric on R. Prove that d is a metric on R?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 39RE
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Let a = (a1, az); b = (b, ,b2) € R², define the function
%3D
%3D
d: R? x R? ---> R by d=(a, b) = |b,-a, I + do(az, b2), where
%3D
do denotes the discrete metric on R. Prove that d is a
metric on R?
Transcribed Image Text:Let a = (a1, az); b = (b, ,b2) € R², define the function %3D %3D d: R? x R? ---> R by d=(a, b) = |b,-a, I + do(az, b2), where %3D do denotes the discrete metric on R. Prove that d is a metric on R?
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