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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.
The term  axiom may also be used to refer to a background assumption. Example of a postulate: Through any two points in a plane there is exactly one straight line. A theorem is a statement that can be proven to be true based upon postulates and previously proven theorems.