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Defects of Properties in Mathematics(v5)
Hardcover
Series: Concrete and Applicable Mathematics, Book 5
Medical ReferenceGeneral Mathematics
ISBN13: 9789810249243
Publisher: World Scientific Publishing Company
Published: Apr 23 2002
Pages: 364
Weight: 1.83
Height: 1.13 Width: 6.00 Depth: 9.00
Language: English
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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