axiomatic set theory

Axiomatic set theory is a branch of mathematics that establishes a framework for understanding sets—a collection of objects. Instead of relying on intuitive ideas, it starts with a small set of basic assumptions, called axioms, which are accepted as true. From these axioms, mathematicians derive theorems and build a consistent theory of sets. A prominent version is Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC), which underpins much of modern mathematics. This rigorous approach helps clarify concepts, avoid paradoxes, and provides a solid foundation for mathematical reasoning.