Center is Element of Open Ball/P-adic Numbers

Theorem
Let $p$ be a prime number.

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

Let $a \in \Q_p$.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

Let $\map {B_\epsilon} a$ be the open $\epsilon$-ball of $a$ in $\struct {\Q_p, \norm {\,\cdot\,}_p}$.

Then:
 * $a \in \map {B_\epsilon} a$

Proof
By definition, $\map {B_\epsilon} a$ is the open $\epsilon$-ball of $a$ in the normed division ring $\struct {\Q_p, \norm {\,\cdot\,}_p}$.

From Center is Element of Open Ball in Normed Division Ring: $a \in \map {B_\epsilon} a$