Definition:Null Sequence/Normed Division Ring
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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 $0_R$:
- $\ds \lim_{n \mathop \to \infty} x_n = 0_R$
Then $\sequence {x_n}$ is called a null sequence.
Sources
- 2007: Svetlana Katok: p-adic Analysis Compared with Real ... (previous) ... (next): $\S 1.2$: Normed Fields, Definition $1.7$