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 $\eqclass {\sequence{x_n}}{}$ be any $p$-adic number of $\Q_p$. That is, $\eqclass {\sequence{x_n}}{}$ is a left coset of $\Q_p$.

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

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.