\begin{definition}[Definition:Null Sequence/Real Numbers]
Let $\sequence {x_n}$ be a sequence in $\R$ which converges to a limit of $0$:
:$\ds \lim_{n \mathop \to \infty} x_n = 0$
Then $\sequence {x_n}$ is called a '''(real) null sequence'''.
\end{definition}