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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.
Definition of arithmetic. 1a : a branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to themb : a treatise on arithmetic.