# Affine set

A set $LaTeX: S$ that contains the line through any two of its points --i.e. $LaTeX: x, y \in S$ implies $LaTeX: ax + (1-a)y \in S$ for all $LaTeX: a \in \mathbb{R}$. The dimension of an affine set is that of the (unique) subspace parallel to it. Dimensions of 0, 1 and 2 are called points, lines and planes, respectively.