Let A be a non-empty subset of Y, and let $\displaystyle x\in y$.

If $\displaystyle d(x,A)=0$

then there is a sequence $\displaystyle x_n$ of points in A such that $\displaystyle x_n$ converges to x.

Can anyone give me a starting point here? Should I try to prove this by contradiction? I'm just unsure of how to prove a sequence exists...