 |
| Starring Rarity as Roger Smith |
Definition:
$f(x) = O(g(x)) \mbox{ as } x \rightarrow \infty$
if and only if
$\exists \, M, x_0 \in \mathbb{R}^+ : |f(x)| \leq M|g(x)| \, \forall x > x_0$
Some basic observations:
-The equality sign here is an odd convention, because this is more of an order relation.
-This isn't a 'total ordering' when we look at all $f$ and $g$; $e^xsin(x)$ and $x^2$ are incomparable.
-There's an obvious analogue of this definition for sequences (those discrete things) and all the results discussed here apply equally to them.
Basic result(s) come after the break.
