Postulate is an assumption that need not to be proved and it is specific to geometry.axiom is an assumption that need not to be proved but it is not related to geometry.

Postulate vs Axioms

Postulates and axioms are both fundamental principles in mathematics used as starting points for further reasoning. While they are often used interchangeably, there is a subtle difference between the two concepts.

Postulates
- Postulates are basic assumptions that are accepted without proof in a particular mathematical system.
- They are considered self-evident truths that serve as the foundation for further mathematical reasoning.
- Postulates are specific to a particular branch of mathematics and are used to derive theorems within that system.
- They are often derived from observations of the physical world or intuitive reasoning.
- Postulates are sometimes referred to as "axioms of geometry" in the context of Euclidean geometry.

Axioms
- Axioms are fundamental statements that are universally accepted as true in all mathematical systems.
- They are self-evident truths that are not proven within the system but are assumed to be true.
- Axioms are more general and abstract than postulates, providing the basis for reasoning in various branches of mathematics.
- They are used to derive theorems and establish the logical consistency of a mathematical theory.
- Axioms are considered to be universal truths that govern the rules of logic and reasoning in mathematics.

In summary, postulates are specific assumptions within a mathematical system, while axioms are general principles that apply universally across different mathematical systems. Both postulates and axioms play crucial roles in the development of mathematical theories and theorems.