\begin{definition}[Definition:Asymptotically Equal/Functions]
Let $f$ and $g$ real functions defined on $\R$.
Then:
: '''$f$ is asymptotically equal to $g$'''
{{iff}}:
:$\dfrac {f \left({x}\right)} {g \left({x}\right)} \to 1$ as $x \to +\infty$.
That is, the larger the $x$, the closer $f$ gets (relatively) to $g$.
Category:Definitions/Asymptotic Notation
Category:Definitions/Real Analysis
\end{definition}