\begin{definition}[Definition:Asymptotically Equal/Sequences/Definition 1]
Let $\sequence {a_n}$ and $\sequence {b_n}$ be sequences in $\R$.
Let $b_n \ne 0$ for all $n$.
$\sequence {a_n}$ is '''asymptotically equal''' to  $\sequence {b_n}$ {{iff}}:
:$\ds \lim_{n \mathop \to \infty} \dfrac {a_n} {b_n} = 1$
\end{definition}