ZFC (Zermelo-Fraenkel set theory with Axiom of Choice)

ZFC is a foundational framework for mathematics based on sets—collections of objects. It includes rules (axioms) that define how sets behave, such as how they can be built, combined, and compared. The Axiom of Choice, an optional part of ZFC, states that given a collection of sets, we can choose one element from each set—even if there’s no explicit rule for doing so. Together, ZFC provides a rigorous basis to develop and understand virtually all mathematical concepts, ensuring consistency and clarity in the foundations of mathematics.