| Defects of Properties in Mathematics: Quantitative Characterizations Contributor(s): Ban, Adrian I. (Author), Gal, Sorin G. (Author) |
|
 |
ISBN: 9810249241 ISBN-13: 9789810249243 Publisher: World Scientific Publishing Company OUR PRICE: $128.25 Product Type: Hardcover Published: April 2002 |
| 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. |