\begin{definition}[Definition:Convergent Sequence/P-adic Numbers/Definition 1]
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 $x \in \Q_p$''' {{iff}}:
:$\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: \forall n \in \N: n > N \implies \norm {x_n - x}_p < \epsilon$
Category:Definitions/Sequences
Category:Definitions/Convergence
Category:Definitions/P-adic Number Theory
\end{definition}