What is an Axiom?
Definitions of Axiom
- An established rule, principle, or law
- A self-evident or universally recognized truth
- A self-evident principle or one that is accepted as true without proof as the basis for argument
Examples of Axioms from Euclidean Geometry
- Each two distinct points determine a (unique) line.
- Three noncollinear points determine a (unique) plane.
- If l is any line and P any point not on l, there exists in the plane of l and P one and only one line m that passes through P and is parallel to l.
Example of an axiom pertinent to the discussion