An axiomatic system is a structured framework in mathematics and logic where a set of basic statements, called axioms, are accepted as true without proof. These axioms serve as the foundation for deriving further statements, known as theorems, through logical reasoning. The goal is to build a coherent system where all conclusions follow logically from the initial axioms. A well-known example of an axiomatic system is Euclidean geometry, which is based on a few fundamental axioms about points, lines, and planes. By applying logical deductions to these axioms, mathematicians can prove various geometric properties and theorems, creating a comprehensive understanding of the subject.