Define a metric $\displaystyle d$ on a set $\displaystyle X$ having more than one element as follows:

For every $\displaystyle x,y \in X$, d(x,y)={1 if x =/= y, 0 if x = y}

Let $\displaystyle b$ in $\displaystyle X$. Give an example that shows the closure of B(b,1) =/= {y in Y : d(b,y)<=1}

NOTE: B(b,1) is an open ball centered at b with radius 1.