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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.
Written By: Axiom, in logic, an indemonstrable first principle, rule, or maxim, that has found general acceptance or is thought worthy of common acceptance whether by virtue of a claim to intrinsic merit or on the basis of an appeal to self-evidence. An example would be: âNothing can both be and not be at the same time and in the same respect.â. 1  In Euclidâs Elements the first principles were listed in two categories, as postulates and as common notions. 2  In modern times, mathematicians have often used the words postulate and axiom as synonyms.