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## Homework Statement

Give an example of a decreasing sequence of closed balls in a COMPLETE metric space with empty intersection.

Hint 1: use a metric on N topologically equivalent to the discrete metric so that {n≥k} are closed balls.

Hint 2: I

_{n}={n,n+1,n+2,...}. Consider the metric d(m,n)=∑1/2

^{k}where the sum is from k=m to k=n-1.

## Homework Equations

N/A

## The Attempt at a Solution

I really have no idea how to do this problem...how can we construct an example that would work?

Any help/hints is greatly appreciated!