A mathematical system is a structured framework that consists of a set of elements and rules for combining them. These systems can include numbers, operations, and relationships, allowing for the exploration of mathematical concepts. Common examples of mathematical systems are arithmetic, algebra, and geometry, each with its own unique properties and rules. In a mathematical system, axioms or postulates serve as the foundational truths from which other statements can be derived. Theorems are then proven based on these axioms, creating a logical structure. This systematic approach helps mathematicians understand and solve complex problems within various fields, including science and engineering.