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An axiom is a mathematical statement that serves as a starting point from which other statements are logically derived.

Axioms cannot be derived or proved; they do not logically follow from anything else (otherwise, they would be called theorems.

The first set of axioms most mathematics students hear of are the axioms of Euclidean geometry, called Euclid's Postulates:

  • It is possible to draw a straight line from any point to any other point.
  • It is possible to produce a finite straight line continuously in a straight line.
  • It is possible to describe a circle with any center and any radius.
  • It is true that all right angles are equal to one another.
  • (The "Parallel Postulate") It is true that, if a straight line falling on two straight lines make the interior angles on the same side less than two angles, the two straight lines, if produced indefinitely, intersect on that side on which are the angles less than the two right angles.
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