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Defects of Properties in Mathematics: Quantitative Characterizations
Contributor(s): Ban, Adrian I. (Author), Gal, Sorin G. (Author)

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 ISBN: 9810249241     ISBN-13: 9789810249243
Publisher: World Scientific Publishing Company
OUR PRICE: $128.25  

Binding Type: Hardcover
Published: April 2002
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Additional Information
BISAC Categories:
- Mathematics | Mathematical Analysis
- Mathematics | Differential Equations - General
- Medical
Dewey: 510
LCCN: 2002514305
Series: Concrete and Applicable Mathematics
Physical Information: 364 pages
 
Descriptions, Reviews, Etc.
Publisher Description:
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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