For given two nonempty sets S$1,$ S$2$ Rn$,$ define the operation S$1+$ S$2$ as follows:

S$1+$ S$2$ :$=\{$z in Rn $|$ there exist some x in S$1$ and some y in S$2$ such that z $=$ x $+$ y $\}$

that is$,$ each point z in S$1+$ S$2$ is the one that can be expressed as the sum x $+$ y for

some x in S$1,$ and y in S$2$; here the sum x$+$y is the vector sum between the two vectors.

One does this for all x in S$1$ and y in S$2$ and get the set S$1+$ S$2.$