Definition:P-adic Number/Representative

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Definition

Let $p$ be any prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Let $\NN$ be the set of null sequences in $\struct {\Q, \norm {\,\cdot\,}_p}$.


Let $\sequence{x_n} + \NN$ be any $p$-adic number of $\Q_p$.

Each Cauchy sequence $\sequence {y_n}$ of the left coset $\sequence{x_n} + \NN$ is called a representative of the $p$-adic number $\sequence{x_n} + \NN$.


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