What is an Axiom?

Definitions of Axiom

  1. An established rule, principle, or law
  2. A self-evident or universally recognized truth
  3. A self-evident principle or one that is accepted as true without proof as the basis for argument

Examples of Axioms from Euclidean Geometry

  1. Each two distinct points determine a (unique) line.
  2. Three noncollinear points determine a (unique) plane.
  3. 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