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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.
Haskell Curry defined mathematics simply as the science of formal systems. A formal system is a set of symbols, or tokens, and some rules telling how the tokens may be combined into formulas. In formal systems, the word axiom has a special meaning, different from the ordinary meaning of a self-evident truth.