Definition:Summation/Inequality/Multiple Indices

Definition
Let $\displaystyle \sum_{0 \mathop \le j \mathop \le n} a_j$ denote the summation of $\left({a_0, a_1, a_2, \ldots, a_n}\right)$.

Summands with multiple indices can be denoted by propositional functions in several variables, for example:


 * $\displaystyle \sum_{0 \mathop \le i \mathop \le n} \left({\sum_{0 \mathop \le j \mathop \le n} a_{i j} }\right) = \sum_{0 \mathop \le i, j \mathop \le n} a_{i j}$


 * $\displaystyle \sum_{0 \mathop \le i \mathop \le n} \left({\sum_{0 \mathop \le j \mathop \le i} a_{i j} }\right) = \sum_{0 \mathop \le j \mathop \le i \mathop \le n} a_{i j}$