Question: Let S be convex set in n that contains no interior points of the non positive orthant n-. Then there exists a hyperplane with nonnegative

Let S be convex set in ℜn that contains no interior points of the non positive orthant ℜn-. Then there exists a hyperplane with nonnegative normal p ≩ 0 such that
pTx ≥ 0 for every x ∈ S

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