Definition:Big-O Notation/Implied Constant

Definition

Let $f$ and $g$ be real functions such that $f$ is big-$\OO$ of $g$.

From the definition of the limit of a function, it can be seen that this is also equivalent to:

$\exists c \in \R: c > 0, k \ge 0: \forall n > k: \map f n \le c \map g n$

For some fixed $k$ (appropriate to the function under consideration) the infimum of such $c$ is called the implied constant.

Work In Progress In particular: rewrite this in a way so it can be transcluded at all definitions of Big-O You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by completing it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{WIP}} from the code.

Also known as

The implied constant is also known as the implicit constant.