Final answer:
An axiom is a statement that is assumed to be true without proof and serves as the foundation of a mathematical system. Axioms are not proven to be true or false, but accepted as true within a specific mathematical framework.
Step-by-step explanation:
An axiom, also known as a postulate, is a statement that is assumed to be true without proof. In mathematics, axioms serve as the foundation of a mathematical system and are used as starting points to derive other mathematical statements or theorems. They are considered to be true within the context of the particular mathematical system being studied.
For example, in Euclidean geometry, one of the axioms is the parallel postulate, which states that given a line and a point not on the line, there is exactly one line through the point that is parallel to the given line. This axiom is taken to be true in the context of Euclidean geometry and is used to derive other geometric results.
It is important to note that axioms are not proven to be true or false, but rather accepted as true within a specific mathematical framework.