[[!redirects Sandbox > history]] [[!redirects Sandbox]] < [[nlab:Sandbox]] Algebraic real analysis. * differentiability - preservation of function by the canonical strictly monotonic ring homomorphism from the Dedekind real numbers into an Archimedean ordered Artinian local Dedekind real algebra, and satisfying the truncated Taylor series condition. * continuity - shapewise continuity: the function graph has contractible shape, contractible localization at the Dedekind real numbers * integration - every closed interval in the Dedekind real numbers is a closed midpoint algebra, see Peter Freyd's algebraic real analysis. category: redirected to nlab