Definition:P-adic Number/Representative

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 $\sequence{x_n} + \NN$.

Also see

 * Leigh.Samphier/Sandbox/Representative of P-adic Number is Representative of Equivalence Class where it is proved that the definition of a representative of a $p$-adic number coincides with the definition of a representative of an equivalence class.