TY  - BOOK
AU  - Dinis,Bruno
AU  - Berg,Imme van den
TI  - Neutrices and external numbers: a flexible number system 
T2  - Monographs and research notes in mathematics
SN  - 9780415016131
AV  - QA299.82 .D56 2019eb
U1  - 511.3/4 23
PY  - 2019///]
CY  - Boca Raton, Florida
PB  - CRC Press
KW  - Nonstandard mathematical analysis
KW  - Model theory
KW  - MATHEMATICS / Functional Analysis
KW  - bisacsh
KW  - MATHEMATICS / Set Theory
KW  - MATHEMATICS / Applied
N2  - 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
UR  - https://www.taylorfrancis.com/books/9780429291456
UR  - http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
ER  -