Definition:Setwise Addition

Definition
Let $\left({S, +}\right)$ be an algebraic structure.

Setwise addition is the operation assigning to two subsets $A,B$ of $S$ their sum:


 * $A + B := \left\{{a + b: a \in A, b \in B}\right\}$

It is customary to denote setwise addition by the same symbol $+$.

When using this construct, it is best to state explicitly that one is dealing with setwise addition.

This is necessary as some sources use $A + B$ to denote set union or disjoint union.