Definition:Asymptotic Equality/Sequences/Definition 3

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

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

where $\oo$ denotes little-$\oo$ notation.

Also see

 * Equivalence of Definitions of Asymptotically Equal Sequences