Definition:Little-O Notation/Notation

Notation for Little-$\oo$ Notation

The expression $\map f n \in \map \oo {\map g n}$ is read as:

$\map f n$ is little-$\oo$ of $\map g n$

Similarly, when expressed in the notation of sequences, $a_n \in \map \oo {b_n}$ is read as:

$a_n$ is little-$\oo$ of $b_n$

While it is correct and accurate to write:

$\map f n \in \map \oo {\map g n}$

or:

$a_n \in \map \oo {b_n}$

it is a common abuse of notation to write:

$\map f n = \map \oo {\map g n}$

or:

$a_n = \map \oo {b_n}$

This notation offers some advantages.