Definition:Summation/Summand/Infinite

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 $A = \set {a_j: j \in \Z} \subseteq S$ be a set of elements of $S$.

Let $\map R j$ be a propositional function of $j$.

Let:
 * $\ds \sum_{\map R j} a_j$

be an instance of a summation on $A$.

Let an infinite number of values of $j$ satisfy $\map R j = \T$.

The set of elements $\set {a_j \in A: \map R j}$ is called an infinite summand.

Also known as
The infinite summand is also known as an infinite set of summands.