\begin{definition}[Definition:Free Matroid]
Let $S$ be a finite set.
Let $\mathscr I = \powerset S$ be the power set of $S$.
That is, let $\mathscr I$ be the set of all subsets of $S$:
:$\mathscr I := \set {X: X \subseteq S}$
Then the ordered pair $\struct{S, \mathscr I}$ is called the '''free matroid of $S$'''.
\end{definition}