The limit points of a subset of binary space with ultra metric

Question

let $Z$ be the subset of binary space $B$ consisting of all points that are eventually $0$. Then what is set of all limit points of $Z$.

Binary Space $(B,d)$ is a metric space as follows. Let $BB$ be the set of all infinite sequences of $0$'s and $1$'s. That is, points of $B$ are of the form $x=(x_1,x_2,x_3, \ldots)$, where $x_i=0$ or $1$ for every $i=1,2,3, \ldots$ . If $x=(x_1,x_2,x_3,\ldots)$, $y=(y_1,y_2,y_3,\ldots)$ belong to $B$, define $d(x,y)=0$ if $x=y$; otherwise $1/n$ if $x$ doesn't equal to $y$ and $n=\min\{i∣x_i \neq y_i\}$.

How can I describe the set of all limit points of $Z$?

I have already found out that $Z$ is neither open nor closed. Thanks in advance.

Answer 1

HINT: Show that $Z$ is dense in $B$.