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  "body": "\n## Definition\n\nLet $V$ be a real [[vector space|000AYPA9AJ]] and let $x, y \\in V$.\nThe *line segment* (or closed segment) between $x$ and $y$ is the set\n$$[x, y] = \\set{(1 - t) x + t y : t \\in \\R,\\ 0 \\le t \\le 1}.$$\nThe points $x$ and $y$ are its endpoints.\n\n## Remarks\n\nExample: in $\\R^2$, the point $(1, 2)$ lies in $[(0, 0), (2, 4)]$, since $(1, 2) = \\tfrac12 (0, 0) + \\tfrac12 (2, 4)$ with $t = 1/2 \\in [0, 1]$.\n\nNon-example: the point $(3, 6)$ lies on the line through $(0, 0)$ and $(2, 4)$, but $(3, 6) = (1 - t)(0,0) + t (2, 4)$ forces $t = 3/2$, which is not in $[0, 1]$.\nSo $(3, 6) \\notin [(0,0), (2,4)]$.\n\nThe segment $[x, y]$ is the set of [[convex combinations|21SXYJYC59]] of $x$ and $y$, and $[x, y] = [y, x]$.\nIf $x = y$, then $[x, y] = \\set{x}$.\n",
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