Axiom
Pronunciation: /ˈæk.si.əm/ Explain
An axiom is a statement that is taken to be
true without proof^{[2]}. 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 

Given
collinear
points A, B, and C, C is between
A and B if AC + CB = AB.
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 

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.
Notice that m∠BAC + m∠CAD
= m∠BAD.

Table 1: Examples of axioms 
References
 McAdams, David E.. All Math Words Dictionary, axiom. 2nd Classroom edition 201501084799968. pg 22. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Mendell, Henry. Aristotle and Mathematics. sect 2. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. Last Accessed 6/12/2018. http://plato.stanford.edu/entries/aristotlemathematics/#2.
 Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 3. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 6/12/2018. http://www.archive.org/stream/mathengineer00kellrich#page/3/mode/1up/search/axiom. Buy the book
More Information
 McAdams, David E.. Euclidean Geometry. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. https://www.allmathwords.org/en/e/euclideangeometry.html.
Cite this article as:
McAdams, David E. Axiom. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/axiom.html.
Image Credits
Revision History
4/12/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
6/15/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (
McAdams, David E.)
1/1/2010: Added "References". (
McAdams, David E.)
10/26/2008: Changed manipulatives from sketchpad to geogebra. (
McAdams, David E.)
10/10/2008: Changed text to compare hypothesis and conjecture, expanded 'More Information'. (
McAdams, David E.)
7/8/2008: Added axiomatic system. (
McAdams, David E.)
4/7/2008: Added More Information. (
McAdams, David E.)
3/25/2008: Added examples. (
McAdams, David E.)
9/3/2007: Added synonym 'postulate'. (
McAdams, David E.)
7/12/2007: Initial version. (
McAdams, David E.)