Definition:Asymptotic Equality/Sequences

Definition
Let $\left \langle {a_n} \right \rangle$ and $\left \langle {b_n} \right \rangle$ be sequences in $\R$.

Then $\left \langle {a_n} \right \rangle$ is asymptotically equal to $\left \langle {b_n} \right \rangle$ iff $b_n\neq0$ for $n$ sufficiently large, and $\dfrac {a_n} {b_n} \to 1$ as $n \to \infty$.