 Similarly, the anti-symmetrization or skew-symmetrization of a map formula_7 is the map formula_10.The sum of the symmetrization and the anti-symmetrization of a map "α" is 2"α".Thus, away from 2, meaning if 2 is invertible, such as for the real numbers, one can divide by 2 and express every function as a sum of a symmetric function and an anti-symmetric function.