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In mathematics or logic, an unprovable rule or first principle accepted as true because it is self-evident or particularly useful (e.g., Nothing can both be and not be at the same time and in the same respect). The term is often used interchangeably with postulate, though the latter term is sometimes reserved for mathematical applications (such as the postulates of Euclidean geometry). It should be contrasted with a theorem, which requires a rigorous proof.
This entry comes from Encyclopædia Britannica Concise. For the full entry on axiom, visit Britannica.com.