Category:Definitions/Asymptotic Equality

This category contains definitions related to Asymptotic Equality.
Related results can be found in Category:Asymptotic Equality.

Sequences

Let $b_n \ne 0$ for all $n$.

$\sequence {a_n}$ is asymptotically equal to $\sequence {b_n}$ if and only if:

$\ds \lim_{n \mathop \to \infty} \dfrac {a_n} {b_n} = 1$

Real Functions

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

Then:

$f$ is asymptotically equal to $g$

if and only if:

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

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