## 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 $x \in \Q_p$ if and only if:

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