Zermelo-Fraenkel Set Theory

Zermelo-Fraenkel Set Theory (ZF) is a foundational system for mathematics that describes how sets—collections of objects—function. It consists of a series of axioms, or rules, that outline how sets can be formed, combined, and related to each other. Key concepts include the existence of an empty set, the ability to create new sets from existing ones, and the idea of infinite sets. ZF helps to prevent paradoxes, ensuring consistency in mathematics. When combined with the Axiom of Choice, it forms ZFC, a widely accepted framework for understanding the nature of sets and their relationships.