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.

Defects of Properties in Mathematics

Science & Math

Gal, Sorin G.

Ban, Adrian I

Mathematics

World Scientific Publishing Company

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Books by Ban, Adrian I

See the best price to sell, buy, or rent books by Ban, Adrian I. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Defects of Properties in Mathematics