Definition:Convergent Sequence/P-adic Numbers/Definition 4

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 $\norm {\, \cdot \,}_p$ :


 * the real sequence $\sequence {\norm {x_n - x}_p }$ converges to $0$ in the reals $\R$

Also see

 * Definition:Convergent Real Sequence