Consider the sequence space . Then, it is easy to prove that
(i) is a distance on .
(ii) If and for then, . Conversely, if , then for .
Try the rest of your questions.
I need to define a metric function "d" on the space (infinite {0,1} sequences)
d must support:
a. get only rational values
b. for every c belongs to C and every the ball of radius contains infinite number of objects.
c. for every a,b belong to C there is an isometric function f : that supports f(a)=b.
I apologize for any spelling mistakes and appreciate your help