  Motivated by intuitive properties of physical quantities, the notion of a
non-anomalous semigroup is formulated. These are totally ordered semigroups
where there are no `infinitesimally close' elements. The real numbers are then
defined as the terminal object in a closely related category. From this
definition a field structure on $\mathbb R$ is derived, relating multiplication
to morphisms between non-anomalous semigroups.
