Neutrices and External Numbers: A Flexible Number System PDF

Neutrices and External Numbers: A Flexible Number System introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations. The model is formulated in terms of scalar neutrices and external numbers, in the form of an extension of the nonstandard set of real numbers. Many illustrative examples are given. The book starts with detailed presentation of the algebraic structure of external numbers, then deals with the generalized Dedekind completeness property, applications in analysis, domains of validity of approximations of solutions of differential equations, particularly singular perturbations. Finally, it describes the family of algebraic laws characterizing the practice of calculations with external numbers.

Features

Presents scalar neutrices and external numbers, a mathematical model of order of magnitude within the real number system.

Outlines complete algebraic rules for the neutrices and external numbers

Conducts operational analysis of convergence and integration of functions known up to orders of magnitude

Formalises a calculus of error propagation, covariant with algebraic operations

Presents mathematical models of phenomena incorporating their necessary imprecisions, in particular related to the Sorites paradox

Authors: Bruno Dinis, Imme van den Berg