Defects of Properties in Mathematics - Hardcover

Ban, Adrian I; Gal, Sorin G

Hardcover

ISBN 10: 9810249241 ISBN 13: 9789810249243

Publisher: World Scientific Publishing Company, 2002

Synopsis

This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics.Besides well-known "defects", the book introduces and studies new ones, such as: measures of noncompactness for fuzzy sets; fuzzy and intuitionistic entropies; the defect of (sub, super)additivity; complementarity; monotonicity for set functions; the defect of convexity; monotonicity; differentiability for real functions; the defect of equality for inequalities; the defect of orthogonality for sets and defects of properties for linear operators in normed spaces; defects of properties (commutativity, associativity, etc.) for binary operations; defects of orthogonality and parallelness in Euclidean and non-Euclidean geometries; defects of integer, perfect, prime and amicable numbers; the defect of tautology in fuzzy logic.

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.,." a good handbook-like source in general mathematics ..."

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2002
• Language: English
• ISBN 10: 9810249241
• ISBN 13: 9789810249243
• Binding: Hardcover
• Edition number: 1
• Number of pages: 364