Definition:Summation over Finite Subset

Definition
Let $G$ be a commutative monoid.

Let $F \subseteq G$ be a finite subset of $G$.

Let $\set{g_1, g_2, \ldots, g_n}$ be a finite enumeration of $F$.

Let $\tuple{g_1, g_2, \ldots, g_n}$ be the ordered tuple formed from $\set{g_1, g_2, \ldots, g_n}$.

The summation over F, denoted $\ds \sum_{g \in F} g$, is defined as the summation over $\tuple{x_1, x_2, \ldots, x_n}$:
 * $\ds \sum_{g \in F} g = \sum_{i = 1}^n g_i$

Also see

 * User:Leigh.Samphier/Topology/Summation over Finite Set is Well-Defined