ZFC (Zermelo-Fraenkel set theory with Choice)

ZFC (Zermelo-Fraenkel set theory with Choice) is a foundational framework for mathematics that describes how sets—collections of objects—are built and interact. It consists of axioms (basic rules) that define how sets are formed, how they relate, and how to handle infinite collections, ensuring consistency and avoiding paradoxes. The "Choice" axiom allows for selecting elements from sets even when no explicit rule exists. Together, ZFC provides a rigorous, logical basis for most of modern mathematics, ensuring all mathematical concepts can be grounded in a well-defined, unified foundation.