[[!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. The latter might not exist. Reverse real analysis. Because there is no one such notion of real numbers in weakly predicative constructive mathematics. category: redirected to nlab