 Note that some authors define cone with the scalar "α" ranging over all non-negative reals (rather than all positive reals, which does not include 0).A cone "C" is a convex cone if belongs to "C", for any positive scalars "α", "β", and any "x", "y" in "C".A cone "C" is convex if and only if "C" + "C" ⊆ "C".