Definition:Convergent Sequence/P-adic Numbers

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 $\Q_p$.

Definition 3
Then $x$ is a limit of $\sequence {x_n}$ as $n$ tends to infinity which is usually written:
 * $\displaystyle x = \lim_{n \mathop \to \infty} x_n$

Also see

 * Definition:P-adic Metric
 * P-adic Metric is Metric
 * Definition:Convergent Real Sequence