Axiom
High school
An axiom is a statement that is accepted without proof as a starting point, from which other statements are proved.
Undergraduate (logic)
Consider a mathematical theory, such as set theory or the theory of groups. An axiom of the theory is a statement that is taken as given, rather than proved, and from which the theory’s theorems are derived.
Properties
- Axioms are not claimed to be true about the world; they define what the theory is about. For example, the group axioms define what a group is.