\begin{definition}[Definition:O Notation/Big-O Notation/Implied Constant]
Let $f$ and $g$ be real functions such that $f$ is big-O of $g$.
From the definition of the limit of a function, it can be seen that this is also equivalent to:
:$\exists c \in \R: c > 0, k \ge 0: \forall n > k, f \left({n}\right) \le c g \left({n}\right)$
For some fixed $k$ (appropriate to the function under consideration) the infimum of such $c$ is called the '''implied constant'''.
{{wtd|rewrite this in a way so it can be transcluded at all definitions of Big-O}}
Category:Definitions/Order Notation
\end{definition}