Affine Dimension
# Definition 1
Let $V$ be a Vector Space over $\mathbb{R}$ and let $S \subset V$ be an Affine Set. Then the Affine Dimension of $S$ is the dimension of the subspace associated with $S$.
# Definition 2
Let $V$ be a Vector Space over $\mathbb{R}$ and let $S \subset V$. Then the Affine Dimension of $S$ is the Affine Dimension of $\mathbf{aff} S$.