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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2016
- DOI:
- 10.48550/arXiv.1607.05997
- arXiv:
- arXiv:1607.05997
- Bibcode:
- 2016arXiv160705997B
- Keywords:
-
- Mathematics - History and Overview;
- Mathematics - Category Theory;
- Mathematics - Rings and Algebras
- E-Print:
- 21 pages