 Order dual

In mathematics, specifically in order theory and functional analysis, the order dual of an ordered vector space "X" is the set formula_1 where formula_2 denotes the set of all positive linear functionals on "X", where a linear function "f" on "X" is called positive if for all "x" in "X", "x" ≥ 0 implies "f"("x") ≥ 0.The order dual of "X" is denoted by "X"+.