Let a = (a1, az); b = (b, ,b2) € R², define the function%3D%3Dd: R? x R? ---> R by d=(a, b) = |b,-a, I + do(az, b2), where%3Ddo denotes the discrete metric on R. Prove that d is ametric on R?

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Answered: Let a = (a, az); b = (b, ,b2) € R?,…

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?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.4: Cicumference And Area Of A Cicle

Problem 22E: What is the limit of mRTS if T lies in the interior of the shaded region?

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Question

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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