# Monoid

A set, $LaTeX: M$, defined on rational vectors, such that: (1) $LaTeX: 0 \in M$, and (2) if $LaTeX: v,$ $LaTeX: w$ are in $LaTeX: M$, then $LaTeX: v+w$ is in $LaTeX: M.$ The monoid is integral if it contains only integer vectors. One can think of a monoid as a discrete analogue of a convex cone.