# Half-line

A half-line is a collection of points of the form $LaTeX: \{t \, {{\bf v}: t \ge 0\}$, where $LaTeX: {\bf v}$ is in $LaTeX: {\mathbb R}^n$ such that $LaTeX: {\bf v} \neq 0$ (some state $LaTeX: \|{\bf v}\|=1$, without loss in generality). Note the half-line is rooted at the origin -- see ray for translation.