Difference Between Axiom and Postulate | Postulate vs Axiom

Axiom vs Postulate

If you have read a mathematics book beyond high school mathematics, you would have undoubtedly encountered at least one of the terms postulate and axiom. Especially in the beginning of some elaborate mathematical proof or theory we find these terms. If you are familiar with Euclid’s Geometry, you know that the entire theory is built on several axioms and postulates. Therefore, they lay the foundation for a remarkable work of mathematics which explains the properties of the space in two and three dimensions. You might also have heard that physicist postulate that there are parallel universes. So what are these all important, but exotic axioms and postulates?

What is an Axiom?

An axiom is something which is considered to be true but without a clearly defined proof. You just know that it is true; everybody agrees with it, but nobody can prove that it is correct or disprove that it is incorrect. In a more formal note, the definition of an axiom can be given as a proposition which is self-evidently true. For example, Euclid’s fifth axiom “The whole is greater than the part” is evident to anybody as a true statement.

What is a Postulate?

A postulate is same as an axiom, a proposition which is self-evidently true. The statement “A straight line segment can be drawn joining any two points” is the first postulate in Euclid’s book “Elements”.

The difference between the terms axiom and postulates is not in its definition but in the perception and interpretation. An axiom is a statement, which is common and general, and has a lower significance and weight. A postulate is a statement with higher significance and relates to a specific field. Since an axiom has more generality, it is often used across many scientific and related fields.

Axiom is an archaic (much) older term while postulate is a new term in mathematics.

What is the difference between Axiom and Postulate?