for all "m" = 1, 2, ... provided that we use the convention formula_3 (this choice is unique). In other words, a "product" formula_4 with no factors at all evaluates to 1. Allowing a "product" with zero factors reduces the number of cases to be considered in many mathematical formulas. Such a "product" is a natural starting point in induction proofs, as well as in algorithms. For these reasons, the "empty product is one" convention is common practice in mathematics and computer programming.