Definition:Summation over Finite Subset

Definition
Let $\struct{G, +}$ be a commutative monoid.

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

Let $\set{e_1, e_2, \ldots, e_n}$ be a finite enumeration of $F$.

Let $\tuple{e_1, e_2, \ldots, e_n}$ be the ordered tuple formed from the bijection $e: \closedint 1 n \to F$.

The summation over F, denoted $\ds \sum_{g \mathop \in F} g$, is defined as the summation over $\tuple{e_1, e_2, \ldots, e_n}$:
 * $\ds \sum_{g \mathop \in F} g = \sum_{i \mathop = 1}^n e_i$

Also see

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