Definition:Sum of Finite Set

Definition

Let $\mathbb A$ be one of the standard number systems $\N, \Z, \Q, \R, \C$.

Let $S \subset \mathbb A$ be a finite subset.

The sum of $S$ is the summation of the identity mapping on $S$ over $S$:

$\ds \sum S = \sum_{s \mathop \in S} s$