Non-Anomalous Semigroups and Real Numbers

Abstract

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.

21 pages