[[!redirects Sandbox > history]] [[!redirects Sandbox]] < [[nlab:Sandbox]] Properties on the real numbers are axioms which could be added to any Archimedean ordered field. So one studies the category of Archimedean ordered fields and strictly monotonic field homomorphisms; the category of notions of real numbers. The initial Archimedean ordered field is the numerical analyst's/computer scientist's real numbers, while the terminal Archimedean ordered field is the geometer's real numbers. category: redirected to nlab