# Affine independence

The set $LaTeX: \{x^0, x^1, \ldots, x^k \}$ is affinely independent if their affine hull is k-dimensional. Equivalently, $LaTeX: \{ x^1-x^0, \ldots, x^k-x^0 \}$ is linearly independent. For n=2, any two distinct vectors are affinely independent (k=1). Three vectors need to form a triangle; otherwise, they are co-linear and are affinely dependent.