Equal balls in metric space Let $x$ and $y$ be points in a metric space and let $B(x,r)$ and $B(y,s)$ be usual open balls. Suppose $B(x,r)=B(y,s)$. Must $x=y$? Must $s=r$? 
What I got so far is that: $$r \neq s \implies x \neq y$$ but that's it.

If we consider a discrete metric space (X,d) and let r,s >1 (r not equal to s) and x,y be distinct elements of X. Then B(x,r) = B(y,s).
