Pronunciation: /ˌkɒn.trəˈdɪk.ʃən/ Explain

A contradiction is a statement that is necessarily false.[2] For example, if a proof starts with the assumption 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").

### References

1. 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
2. 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
3. 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.

McAdams, David E. Contradiction. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/contradiction.html.

### Revision History

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.)