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Conjectures and Counterexamples

Learn how to make educated guesses, or conjectures, to problems, as well as how to disprove incorrect guesses with counterexamples.

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The Exception Disproves the Rule

Credit: Pete Souza
Source: http://en.wikipedia.org/wiki/File:Barack_Obama_addresses_joint_session_of_Congress_2009-02-24.jpg
License: CC BY-NC 3.0

Have you ever wondered why politicians and lawyers spend so much time poking holes in their opponents' arguments? Sometimes, it’s easier to prove that someone else is wrong than to prove that your position is correct. All you need is a single counterexample, and you can disprove a faulty example.

Why It Matters

People make conjectures all the time. By drawing on our experiences, we can make accurate predictions about the world around us. However, sometimes our conjectures are wrong. Scientists and other researchers look for counterexamples to popular conjectures. Sometimes, they make discoveries that force us to look at the world in new ways.

Credit: Paul Mannix
Source: http://www.flickr.com/photos/paulmannix/321426642/
License: CC BY-NC 3.0

The Greek philosopher Aristotle believed that heavier objects fell faster than lighter ones. His conjecture made sense to many people. After all, a feather falls more slowly than a rock. However, in 1589 the scientist Galileo dropped two balls of different weights off the top of the Leaning Tower of Pisa. They landed at exactly the same time! Aristotle must have been wrong. Even though Galileo disproved Aristotle’s conjecture in the 16th century, people still make the same mistake today.

See for yourself: https://www.youtube.com/watch?v=aRhkQTQxm4w

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Read the article below to learn about another time scientists disproved a well-known conjecture.


Why would it be easier to disprove a conjecture than to prove one?

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