Closed Balls Centered on P-adic Number is Countable

Theorem
Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Let $a \in \Q_p$.

Then the set of all closed balls centered on $a$ is the countable set:
 * $\displaystyle \mathcal B^{\, -} = \set{\map {B^{\, -}_{p^{-n}}} a : n \in \Z}$