P-adic Numbers form Completion of Rational Numbers with P-adic Norm


 * Completion of Normed Division Ring for a proof that $\struct {\Q_p, \norm {\,\cdot\,}_p}$ is the completion of $\struct {\Q, \norm {\,\cdot\,}_p}$.


 * Completion Theorem for a proof that the completion of $\struct {\Q, \norm {\,\cdot\,}_p}$ exists and is unique up to isometric isomorphism.