Question

Does d(x,y) = | sin( x-y) | , x, y ïr, define a metric for r ? Justify.

Answer 1

2) The Euclidean metric d (or d2) on R* is defined by 11 X (x, - y;)*, i-1 d(x, y) = where x = (x1, . . . , xm), y = (y1,. . . , yn) e IR" (if n = 1, d (x, y) = |x – y|. the metric

Answer 2

Answer: No, it's not a metric on R.

Step-by-step explanation:

d(x,y) = 0

=> |sin (x-y)| =0

=> sin (x-y) =0

=> x-y = k(pi), where k is an integer.

Hence, d(x,y) =0 does not imply x=y.

Therefore, d(x,y) is not a metric on R.