Definition:Limit of Sequence/P-adic Numbers
< Definition:Limit of Sequence(Redirected from Definition:Limit of P-adic Sequence)
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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 $\Q_p$.
Let $\sequence {x_n}$ converge to $x \in \Q_p$
Then $x$ is a limit of $\sequence {x_n}$ as $n$ tends to infinity which is usually written:
- $\ds x = \lim_{n \mathop \to \infty} x_n$