# Axiom

- a saying that widely accepted on its own merits

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

- A basic assumption about a mathematical system from which theorems can be deduced. For example, the system could be the points and lines in the plane. Then an axiom would be that given any two distinct points in the plane, there is a unique line through them.

- (postulate) In a mathematical or logical system, an initial proposition or statement that is accepted as true without proof and from which further statements, or theorems, can be derived. In a mathematical proof, the axioms are often well-known formulae for which the proof has already been established.

- A proposition formally accepted without demonstration, proof, or evidence as one of the starting-points for the systematic derivation of an organized body of knowledge.

- An established rule or principle or a self-evident (obvious) truth.

- n. A self-evident or universally recognized truth maxim. An established rule, principle or law.

- A basic assumption underlying a theory or branch of mathematics.

- Logical condition constraining the behaviour of an object. May be expressed as an invariant, or as a precondition or postcondition on one of the object's methods.