I am trying to prove the following.
$C$ is a nonempty convex subset of $\mathbb{R}^n$. Show that $\operatorname{dim}(\operatorname{aff}(C))$ is the maximum of the dimensions of the simplexes contained in $C$.
Where $\operatorname{dim}(\operatorname{aff}(C))$ refers to the dimension of the affine hull of the convex set C. I know that $\operatorname{dim}(\operatorname{aff}(C))$ = $\operatorname{dim}(C)$ but couldn't figure out how to form the proof. Any help would be appreciated.