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").
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
All Math Words Encyclopedia is a service of
Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License