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Definition of Axiom. Axiom is a rule or a statement that is accepted as true without proof. An axiom is also called a postulate. Examples of Axiom. Here is an axiom of addition and multiplication. Let x and y be real numbers. Then x + y is also a real number and xy is also a real number.
A finite sequence of well-formed formulas, F1, F2, ... Fn, where each Fi either is an axiom, or follows by some rule of inference from some of the previous F's, and Fn is the statement being proved. See also proof theory.