Sanjib Khadka, Xavier’s College, Nepal
Set theory, as the mathematical study of collections of objects, forms a cornerstone of modern mathematical logic, computation, and systems theory. This paper explores set theory's foundational principles, including subsets, unions, intersections, power sets, and Cartesian products, highlighting its role in advanced mathematical concepts and computational frameworks. It also explores the multifaceted domain of set theory, laying a foundation by tracing its historical roots and exa mining its fundamental principles. We delve into the axiomatic framework underpinning set theory, including the ZermeloFraenkel axioms and the Axiom of Choice. The discussion extends to the intricate concepts of cardinality, ordinality, and the continuum hypothesis. Emphasizing pr actical relevance, we highlight the application of set theory , focusing on fuzzy sets, rough sets, and their roles in decision-making and control systems.
Set Theory, Zermelo-Fraenkel Axioms, Axiom of choice, Fuzzy sets, Rough sets, Cardinality, Ordinality, Continuum Hypothesis..
