Axiom (mathematics)

An axiom in mathematics is a fundamental statement or assumption that is accepted as true without proof. It serves as the starting point for building a logical and consistent system of mathematical rules and theories. Axioms are not proven within the system; instead, they are chosen because they are clear, self-evident, or useful for developing the mathematical framework. Different systems may have different sets of axioms. They provide the foundation upon which theorems—a.k.a. proven statements—are based, ensuring clarity and consistency throughout mathematical reasoning.