\begin{definition}[Definition:Matroid Induced by Affine Independence]
Let $\R^n$ be the $n$-dimensional real Euclidean space.
Let $S = \set{x_1, \dots, x_r}$ be a finite subset of $\R^n$.
Let $\mathscr I$ be the set of affinely independent subsets of $S$.
Then $\struct{S, \mathscr I}$ is called the '''matroid induced by affine independence on $S$'''.
\end{definition}