Question

What's the difference between postulate and axioms.

Answer 1

An axiom is a statement, usually considered to be self-evident, that assumed to be true without proof. It is used as a starting point in mathematical proof for deducing other truths.

Classically, axioms were considered different from postulates. An axiom would refer to a self-evident assumption common to many areas of inquiry, while a postulate referred to a hypothesis specific to a certain line of inquiry, that was accepted without proof. As an example, in Euclid's Elements, you can compare "common notions" (axioms) with postulates.

In much of modern mathematics, however, there is generally no difference between what were classically referred to as "axioms" and "postulates". Modern mathematics distinguishes between logical axioms and non-logical axioms, with the latter sometimes being referred to as postulates.