ZF

ZF, or Zermelo-Fraenkel set theory, is a foundational framework for mathematics that describes how sets—collections of objects—are built and related. It provides precise rules (axioms) for constructing and working with sets, ensuring consistency and avoiding paradoxes. Think of it as a rigorous blueprint for mathematics, ensuring that all mathematical concepts and objects are grounded in a well-defined system. ZF is widely used because it underpins most modern mathematical theories, offering clarity and structure to understand complex mathematical ideas in a formal way.