For each nonnegative integer "k", the elementary symmetric polynomial "e""k"("X"1, …, "X""n") is the sum of all distinct products of "k" distinct variables. (Some authors denote it by σ"k" instead.) For "k" = 0 there is only the empty product so "e"0("X"1, …, "X""n") = 1, while for "k" > "n", no products at all can be formed, so "e""k"("X"1, "X"2, …, "X""n") = 0 in these cases. The remaining "n" elementary symmetric polynomials are building blocks for all symmetric polynomials in these variables: as mentioned above, any symmetric polynomial in the variables considered can be obtained from these elementary symmetric polynomials using multiplications and additions only. In fact one has the following more detailed facts: