Category:Convergent P-adic Sequences
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This category contains results about convergent $p$-adic sequences.
Definitions specific to this category can be found in Definitions/Convergent P-adic Sequences.
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 $x \in \Q_p$ if and only if:
- $\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: \forall n \in \N: n > N \implies \norm {x_n - x}_p < \epsilon$
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