Question

let R be the set of real numbers and d :RxR be a metric on R defined by d(x,y)=|x-y|.
obtain d(x,2x)

Answer 1

\(d(x,2x)=|x-2x|=|-x|=|x|\)

Answer 2

thank you sir

Answer 3

can i then say that |x|= norm of x which is (x*x)^1/2 ?

Answer 4

i have another question sir'

Answer 5

\[\let x=R^2 and d \infty : XxX---> R on X define by d \infty(X,Y)=MAX lei \le2|\Xi,Yi| for all X=(x1-x2), Y=(y1-y2). obbtain d \infty(X,Y) if X=(-1,2) and Y=(3,-4)\]

Answer 6

I can't read that. You can always make a metric a norm.

Answer 7

OK. thank u sir