ZFC stands for Zermelo-Fraenkel set theory with the Axiom of Choice, a foundational system for mathematics. It provides a framework for understanding sets, which are collections of objects. ZFC is widely accepted among mathematicians and serves as a basis for much of modern mathematical theory. The axioms of ZFC define how sets behave and interact, allowing for the construction of various mathematical structures. The Axiom of Choice, a key component, states that given a collection of non-empty sets, it is possible to select one element from each set. This principle has significant implications in various areas of mathematics.