Defects Of Properties In Mathematics: Quantitative Characterizations
- Editore:
World Scientific
- EAN:
9789810249243
- ISBN:
9810249241
- Pagine:
- 364
- Formato:
- Hardback
- Lingua:
- Inglese
Descrizione Defects Of Properties In Mathematics: Quantitative Characterizations
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.