Definition:Convergent Sequence/P-adic Numbers/Definition 1

Definition
Let $p$ be a prime number.

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

Let $\sequence {x_n} $ be a sequence in $\Q_p$.

The sequence $\sequence {x_n}$ converges to $x \in \Q_p$ in the norm $\norm {\, \cdot \,}_p$ :


 * $\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: \forall n \in \N: n > N \implies \norm {x_n - x}_p < \epsilon$