# Extreme ray

An extreme ray of a closed set $LaTeX: S$ is a ray in $LaTeX: S$ that cannot be expressed as a (simple) sum of other rays in $LaTeX: S$. For example, the axes, $LaTeX: \{t e_j: t \ge 0\}$, are extreme rays of the non-negative vectors in $LaTeX: \mathbb{R}^n$. The ray $LaTeX: \{t e: t \ge 0\}$, however, is the sum of the axes since $LaTeX: (t,...,t) = t e_1 + \ldots + t e_n$. The recession direction of an extreme ray is sometimes called an extreme direction.