Definition:Asymptotic Equality/Real Functions/Infinity

Definition
Let $f$ and $g$ real functions defined on $\R$.

Then:
 * $f$ is asymptotically equal to $g$ as $x \to \infty$


 * $\dfrac {\map f x} {\map g x} \to 1$ as $x \to +\infty$.
 * $\dfrac {\map f x} {\map g x} \to 1$ as $x \to +\infty$.

That is, the larger the $x$, the closer $f$ gets (relatively) to $g$.