Definition:Asymptotic Equality/Sequences/Definition 1

Definition
Let $\left \langle {a_n} \right \rangle$ and $\left \langle {b_n} \right \rangle$ be sequences in $\R$. Let $b_n \ne 0$ for all $n$.

$\left \langle {a_n} \right \rangle$ is asymptotically equal to $\left \langle {b_n} \right \rangle$ :
 * $\displaystyle \lim_{n\to\infty}\dfrac {a_n} {b_n} \to 1$