\begin{definition}[Definition:Rank (Matroid)]
Let $M = \struct{S, \mathscr I}$ be a matroid.
Let $\rho : \powerset S \to \Z$ be the rank function of $M$.
 
The '''rank''' of $M$, denoted by $\map \rho M$, is the image of $S$ under $\rho$, that is:
:$\map \rho M = \map \rho S$.
\end{definition}