Definition 13.1.8 (Affine Hull).label Let $c\suf \R^{n}$ be nonempty then the affine hull of $c$, denoted $Aff(c)$, is the set of all affine combination of points of $c$. $Aff(c)$ is the smallest affine set containing $c$ so we define $\dim(c)\define \dim(Aff(c))$