# Definition:Null Sequence/Normed Division Ring

## Definition

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 $0_R$:

$\displaystyle \lim_{n \mathop \to \infty} x_n = 0_R$

Then $\sequence {x_n}$ is called a null sequence.