\begin{definition}[Definition:Affinely Dependent/Independent]
Let $\R^n$ be the $n$-dimensional real Euclidean space.
Let $X = \set {x_1, \dots, x_r}$ be a finite subset of $\R^n$.
The subset $X$ is '''affinely independent''' if no element $x \in X$ is affinely dependent on $X \setminus \set x$.
\end{definition}