Definition of Affine Independence
Definition 1
A set of vectors $S := \left\{ v_{0} , v_{1}, \cdots , v_{n} \right\} \subset V$ is said to be Affinely Independent if the vectors in $S$ or $S$ itself are linearly independent. $$ v_{1} - v_{0} , v_{2} - v_{0} , \cdots , v_{n} - v_{0} $$