**Axiom vs. Theorem**

What is Difference between Axiom and Theorem? The terms “axiom” and “theorem” are often used in fields of study such as mathematics, physics and logic. Both have a certain relationship, but it is important to understand that they are not synonymous words; therefore, do not describe the same.

**Difference between Axiom and Theorem**

To clarify a bit the confusion you may have about this topic, here’s what the difference between axiom and theorem is.

**Axiom**

An axiom is an assertion that is accepted as true without the need for it to be proved. It requires no proof and is universally accepted, since its non-acceptance would contradict all logic.

Axioms have no contradiction and are obvious to anyone without the need for any in-depth analysis of things. Some examples of axioms are as follows:

- The whole is greater than any of its parts.
- A proposition cannot be true and false at the same time.
- Two straight lines cannot enclose a space.

**Theorem**

On the other hand, theorems are theoretical proposals that require a check. Unlike axioms, they are not automatically accepted, but are subjected to tests from which the results that support the theory are extracted.

Theorems are made up of two parts: hypotheses and conclusions. Among the examples of theorems one of the best known is the Pythagorean Theorem.