I've been told to find a metric space and two balls in it such that the ball with the smaller radius contains but is not equal to the ball with the larger radius
So I understand this means find such that with and (I realize they do not have to be centered at the same point, but I do not believe assuming so affects the generality if I can find an example like this)
I can't get anywhere. I only know of the euclidean metric, the taxicab metric, the square metric, and the discrete metric, and my professor said that I'd have to consider subsets and restrictions of the distance function is some way....
I don't need a complete answer, just a push in the right direction, thanks