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Tous Homework 1 Special Topics In Math 1. a) Define d (x,y) = 1x²-y²1, X,Y ER. Is da metric on R? 16) Define d (x,y) = 1x²y³l, x, yER. Is d a metvic on R? (a) Defn: Let A be a non-empty set then the function d: AXA - Risa metric on A if

Tous Homework 1 Special Topics In Math 1. a) Define d (x,y) = 1x²-y²1, X,Y ER. Is da metric on R? 16) Define d (x,y) = 1x²y³l, x, yER. Is d a metvic on R? (a) Defn: Let A be a non-empty set then the function d: AXA - Risa metric on A if

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1 a) solved. Could you solve problem 1 b)?

Antonious Homework 1 Special Topics In Math 1. a) Define d (x, y) = 1x²-y²1, x,y ER. Is da metvic on f 16) Define d (x,y) = 1x²=9³1, x, yER. Is d a metvic on 1R? a) Defn: Let A be a non-empty set then the function d: AXA D Risa metric on A if (i) d (x,y) = x,yεA. ii) d (x,y) = dly,x) X,YEA. (iii) d (x₁2) ≤ d (x,y)) + d(y, z) x,y,ZE A. iv) d (x,y) >0 if x#y Here X=IR and dixiy) = |x²y²| Note that, for x=5₁ y = -5. We have dis,-5)= ((51²-1-51²| =125-25)=0. Thus, 5-5 but d (5-5)=0. :. By above dean property iv) fails for d(x₁y) = ( x²_y²³1.
Transcribed Image Text:Antonious Homework 1 Special Topics In Math 1. a) Define d (x, y) = 1x²-y²1, x,y ER. Is da metvic on f 16) Define d (x,y) = 1x²=9³1, x, yER. Is d a metvic on 1R? a) Defn: Let A be a non-empty set then the function d: AXA D Risa metric on A if (i) d (x,y) = x,yεA. ii) d (x,y) = dly,x) X,YEA. (iii) d (x₁2) ≤ d (x,y)) + d(y, z) x,y,ZE A. iv) d (x,y) >0 if x#y Here X=IR and dixiy) = |x²y²| Note that, for x=5₁ y = -5. We have dis,-5)= ((51²-1-51²| =125-25)=0. Thus, 5-5 but d (5-5)=0. :. By above dean property iv) fails for d(x₁y) = ( x²_y²³1.
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