Theorem vs. Axiom

Theoremnoun

(mathematics) A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called lemmas.

Theoremnoun

A mathematical statement that is expected to be true

Theoremnoun

(logic) A syntactically correct expression that is deducible from the given axioms of a deductive system.

Theoremverb

(transitive) To formulate into a theorem.

Theoremnoun

That which is considered and established as a principle; hence, sometimes, a rule.

Theoremnoun

A statement of a principle to be demonstrated.

Theoremverb

To formulate into a theorem.

Theoremnoun

a proposition deducible from basic postulates

Theoremnoun

an idea accepted as a demonstrable truth

Theorem

In mathematics and logic, a theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems. A theorem is hence a logical consequence of the axioms, with a proof of the theorem being a logical argument which establishes its truth through the inference rules of a deductive system.

Axiomnoun

(philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.

Axiomnoun

A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).

Axiomnoun

An established principle in some artistic practice or science that is universally received.

Axiomnoun

A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, "The whole is greater than a part;" "A thing can not, at the same time, be and not be."

Axiomnoun

An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.

Axiomnoun

a saying that widely accepted on its own merits

Axiomnoun

(logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident

Axiomnoun

a statement or proposition which is regarded as being established, accepted, or self-evidently true

Axiomnoun

a statement or proposition on which an abstractly defined structure is based.

Axiom

An axiom, postulate or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'The term has subtle differences in definition when used in the context of different fields of study.