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  "body": "\n## Summary\n\nA positive cone in a real [[vector space|000AYPA9AJ]] is a subset closed under addition and under multiplication by nonnegative scalars.\nIt must also contain no line through the origin.\nPositive cones are the same thing as compatible partial orders: the cone is the set of elements that are at least $0$.\nSo one can describe an order on a vector space just by saying which vectors are positive.\nThe same name is used for the set of nonnegative elements of an ordered group, ring or field.\n\n## Explanations\n\n### L1 human\n\nIn the plane, take the quarter plane of points with both coordinates nonnegative.\nAdding two such points, or stretching one by a nonnegative factor, gives another such point.\nThe quarter plane contains no full line through the origin.\nSaying that $u \\le v$ when $v - u$ lies in the quarter plane gives the componentwise order.\n",
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