Axiom

Pronunciation: /ˈæksiəm/ ?

An axiom is a statement that is taken to be true without proof[1]. An axiom is taken to be self-evidently true, or obviously true. In contrast, a conjecture and a hypothesis are believed to be true, but are not self-evident.

In math, all proofs start directly or indirectly with one or more axioms. The word postulate means the same thing as axiom. An axiomatic system is a logical system that is based on axioms.

Examples

NameRepresentationDescription
Betweenness Assumption
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Manipulative 1: Betweeness Assumption Created with GeoGebra.
Given collinear points A, B, and C, C is between A and B if AC + CB = AB.

Click on the blue points in manipulative 1 and drag them to change the figure. Notice that if C is between A and B that AC + CB = AB. If C is not between A and B then AC + CB > AB.

Angle Addition Postulate
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Manipulative 2: Angle addition postulate. Created with GeoGebra.
If two angles are adjacent, they can be added together to form a larger angle. The measure of the larger angle is the sum of the measures of the two smaller angles.

Click on the blue points in manipulative 2 and drag them to change the figure. Notice that m∠BAC + m∠CAD = m∠BAD.

Table 1: Examples of axioms

References

  1. axiom. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=axiom&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Mendell, Henry. Aristotle and Mathematics, sect 2. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. (Accessed: 2009-12-16). http://plato.stanford.edu/entries/aristotle-mathematics/#2.
  3. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 3. D. Van Nostrand Company, 1908. (Accessed: 2010-01-02). http://www.archive.org/stream/mathengineer00kellrich#page/3/mode/1up/search/axiom.

More Information

  • McAdams, David. Euclidean Geometry. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Euclidean Geometry.
  • Peil, Timothy. Introduction to Axiomatic Systems. 2010-01-16. http://www.mnstate.edu/peil/geometry/C1AxiomSystem/AxiomaticSystems.htm.

Printed Resources

Cite this article as:


Axiom. 2010-01-01. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/axiom.html.

Translations

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Revision History


2010-01-01: Added "References" (McAdams, David.)
2008-10-26: Changed manipulatives from sketchpad to geogebra (McAdams, David.)
2008-10-10: Changed text to compare hypothesis and conjecture, expanded 'More Information' (McAdams, David.)
2008-07-08: Added axiomatic system (McAdams, David.)
2008-04-07: Added More Information (McAdams, David.)
2008-03-25: Added examples (McAdams, David.)
2007-09-03: Added synonym 'postulate' (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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