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

• Summation over Finite Subset is Well-Defined

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