Axiom
Pronunciation: /ˈæksiəm/ ?
An axiom is a statement that is taken to be
true without proof^{[1]}. An axiom is taken to be selfevidently true, or obviously true.
In contrast, a
conjecture
and a
hypothesis
are believed to be true, but are not selfevident.
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
Name  Representation  Description 
Betweenness Assumption 

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 

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
 axiom. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 20110108). http://wordnetweb.princeton.edu/perl/webwn?s=axiom&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
 Mendell, Henry. Aristotle and Mathematics, sect 2. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. (Accessed: 20091216). http://plato.stanford.edu/entries/aristotlemathematics/#2.
 Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 3. D. Van Nostrand Company, 1908. (Accessed: 20100102). 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. 20090312. http://www.allmathwords.org/article.aspx?lang=en&id=Euclidean Geometry.
 Peil, Timothy. Introduction to Axiomatic Systems. 20100116. http://www.mnstate.edu/peil/geometry/C1AxiomSystem/AxiomaticSystems.htm.
Printed Resources
Cite this article as:
Axiom. 20100101. 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
20100101: Added "References" (
McAdams, David.)
20081026: Changed manipulatives from sketchpad to geogebra (
McAdams, David.)
20081010: Changed text to compare hypothesis and conjecture, expanded 'More Information' (
McAdams, David.)
20080708: Added axiomatic system (
McAdams, David.)
20080407: Added More Information (
McAdams, David.)
20080325: Added examples (
McAdams, David.)
20070903: Added synonym 'postulate' (
McAdams, David.)
20070712: Initial version (
McAdams, David.)