Definition:Summation/Finite

Definition
Let $\struct {S, +}$ be an algebraic structure where the operation $+$ is an operation derived from, or arising from, the addition operation on the natural numbers.

Let the set of values of $j$ which satisfy the propositional function $\map R j$ be finite.

Then the summation $\ds \sum_{\map R j} a_j$ is described as being a finite summation.