EUCLIDEAN NUMBERS AND NUMEROSITIES
Vieri Benci, Lorenzo Luperi Baglini
Abstract
Abstract Several different versions of the theory of numerosities have been introduced in the literature. Here, we unify these approaches in a consistent frame through the notion of set of labels, relating numerosities with the Kiesler field of Euclidean numbers. This approach allows us to easily introduce, by means of numerosities, ordinals and their natural operations, as well as the Lebesgue measure as a counting measure on the reals.
Topics & Concepts
MathematicsEuclidean geometrySet (abstract data type)Measure (data warehouse)Euclidean distanceFrame (networking)Computer scienceGeometryData miningTelecommunicationsProgramming languageMathematical and Theoretical AnalysisNumerical Methods and AlgorithmsComputability, Logic, AI Algorithms