Pronunciation: /ˌkɒn.trəˈdɪk.ʃən/ Explain
A contradiction is a statement that is necessarily
false. For example, if a proof starts with the
that line segment AB
is less than line segment CD,
and later concludes that
AB = CD,
both statements can not be true at the same
time. One statement contradicts the other.
A proof by contradiction starts with a statement
that is to be disproved. It then proceeds to show the statement false by arriving at a
contradiction. An example of a proof by contradiction is Euclid's proof that
if two angles are equal, then the sides opposite
the equal angles are also equal. A proof by contradiction can also be called an
indirect proof, or reductio ad absurdum
(Latin for "reduction to the absurd").
- McAdams, David E.. All Math Words Dictionary, contradiction. 2nd Classroom edition 20150108-4799968. pg 45. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Cupillari, Antonella. Nuts and Bolts of Proof: An Introduction to Mathematical Proofs. 3rd edition. pp 22-24. Academic Press. August 15, 2005. Last Accessed 6/25/2018. Buy the book
- Larry W. Cusick. Proofs by Contradiction. California State University, Fresno. Last Accessed 6/25/2018. http://zimmer.csufresno.edu/~larryc/proofs/proofs.contradict.html.
- Euclid of Alexandria. Elements. Clark University. 9/6/2018. https://mathcs.clarku.edu/~djoyce/elements/elements.html.
Cite this article as:
McAdams, David E. Contradiction. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/contradiction.html.
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/5/2010: Added "References". (McAdams, David E.)
6/16/2008: Added text on 'indirect proof' and 'more information'. (McAdams, David E.)
9/17/2007: Initial version. (McAdams, David E.)