Affine Set

Last updated Nov 1, 2022

Let $V$ be a Vector Space over $\mathbb{R}$ and $S \subset V$. $S$ is an Affine Set if for all $\lambda \in \mathbb{R}$ and all $u, v \in S$ $$\lambda u + (1 - \lambda) v \in S$$

1. $S$ is an Affine Set If and Only If $S$ contains all Lines between its points. This is just a restatement of the definition of a Affine Set.

• Real Numbers