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Dinis, Bruno,

Neutrices and external numbers : a flexible number system / Bruno Dinis, Imme van den Berg. - 1 online resource. - Monographs and research notes in mathematics .

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

ISBN: 9780415016131 0415016134 9781000005387 1000005380 9780429291456 0429291450 9781000018721 1000018725 9781000012200 1000012204

Standard No.: 10.1201/9780429291456 doi

Subjects--Topical Terms:
Nonstandard mathematical analysis.
Model theory.
MATHEMATICS / Functional Analysis
MATHEMATICS / Set Theory
MATHEMATICS / Applied

LC Class. No.: QA299.82 / .D56 2019eb

Dewey Class. No.: 511.3/4