Definition:Addition

Naturally Ordered Semigroup
Let $\left({S, \circ, \preceq}\right)$ be a naturally ordered semigroup.

Then the operation $\circ$ in $\left({S, \circ, \preceq}\right)$ is called addition.

Also see

 * Identity Element of Addition on Numbers
 * Inverse Elements for Addition on Numbers


 * Quaternion Addition