\begin{definition}[Definition:Null Sequence/Normed Division Ring]
Let $\struct {R, \norm {\,\cdot\,} }$ be a normed division ring with zero $0_R$.
Let $\sequence {x_n}$ be a sequence in $R$ which converges to the limit $0_R$:
:$\ds \lim_{n \mathop \to \infty} x_n = 0_R$
Then $\sequence {x_n}$ is called a '''null sequence'''.
\end{definition}