Difference between theorem and axiom

A theorem is a stipulation that asserts a truth that is justifiable. An axiom is a proposition taken within a body of theory and other arguments and propositions are based on it.


It is taken as a proposition asserting a justifiable truth. For mathematics, it is any proposition that, starting from an assumption or hypothesis, signs a reasonableness that is not self-evident.

A theorem is believed to be a formula that can be proved within a system from axioms and other theorems. Proving theorems is the main goal of mathematical logic.

Theorems have a number of premises that must be clarified or listed beforehand. The conclusion of a theorem is a logical statement that is true under the conditions generated. A theorem is the relationship between the hypothesis and the thesis or conclusion.


It is a proposition that is assumed within a theoretical body and on it are other arguments and propositions derived from its premises. This notion was introduced by the Greek mathematicians of the Hellenistic period.

The axioms were taken as self-evident propositions and accepted without needing a previous proof. Later, in the hypothetical-deductive system, the axioms were all those propositions not deduced from others, but rather it was the general rule of logical thought.

The axioms are taken to be true statements in any possible world, under any possible interpretation, and under any value comment.

Difference Between Axiom and Theorem

  • An axiom is a statement that is accepted as true without needing to be verified. It does not require proof and is universally accepted. His non-acceptance contradicts any logic.
  • The axioms do not possess a contradiction and are self-evident without recondite analysis.
  • A theorem is a theoretical proposition that requires verification.
  • Theorems are not accepted until they are subjected to tests with results that support the theory.

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