Axiom

An axiom is a statement or proposition that is accepted as being self-evidently true, without the need for proof. Axioms serve as the foundational truths or starting points from which a mathematical or logical system is developed.

Axioms should not be confused with theorems, which are statements that require a proof, typically derived from the axioms of the system. In other words, axioms are the starting points, while theorems are the end points.

Theorem

A theorem is a statement that has been proven to be true within the framework of a mathematical system, based on the system's axioms and previously established theorems.