What is an Axiom in Math? Definition and Examples

What is an axiom in math? An axiom or postulate is an accepted statement that requires no proof. In fact the word axiom comes from the Greek word ἀξίωμα that can have the following meanings:

  • that which is thought fit or worthy
  • that which is considered self-evident 
  • that which a pupil is required to know beforehand

Examples of axioms or accepted statements that require no proof

1. If two lines intersect, then they intersect in exactly one point

One point of intersection

2. Two points are always located on the same line

3. Humans cannot hold their breath for more than half an hour.

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