 Let the sequence formula_1 take values in formula_12.Then the event that the series formula_13 converges (to a finite value) is a symmetric event in formula_3, since its occurrence is unchanged under transpositions (for a finite re-ordering, the convergence or divergence of the series—and, indeed, the numerical value of the sum itself—is independent of the order in which we add up the terms).Thus, the series either converges almost surely or diverges almost surely.