Definition:Asymptotically Equal/Sequences/Definition 3

Definition
Let $\sequence {a_n}$ and $\sequence {b_n}$ be sequences in $\R$.

$\sequence {a_n}$ is asymptotically equal to $\sequence {b_n}$ :
 * $a_n - b_n = \map o {a_n}$

where $o$ denotes little-o notation.