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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.

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