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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.
If there are no statements that the arguer and audience can both. agree on, or at the very least accept for the sake of argument, then there is no way that the. theorist can further his argument in the axiomatic method. In math, axioms are generally basic statements about the elements of a system.