Definition:Convergent Sequence/P-adic Numbers/Definition 2

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 the limit $x \in \Q_p$ :


 * $\sequence {x_n}$ converges to $x$ in the $p$-adic norm

Also see

 * Definition:P-adic Norm
 * P-adic Norm is Norm
 * Definition:Convergent Sequence in Normed Division Ring