Types of Proofs
In this lesson, we learn about several types of proofs and their differences. The most common types of proofs discussed are direct proofs, indirect proofs, proofs by contradiction, trivial proofs, vacuous proofs, and proofs by exhaustion. The lesson provides examples for each type of proof and explains how to use them to prove statements true or false. The lesson also includes a famous proof by contradiction for the irrationality of the square root of 2 and a proof by contradiction for the infinitude of prime numbers.
A brief introduction to several types of proofs and simple examples of each type. Several proofs of each type are worked through, and differences between types of proofs are examined. Now, you can finally understand how different proofs are different, what a proof is, and how to complete different proofs.
- Lesson Slides - Slides that are written on from the lesson.
- How do you prove something?
- How do you write a proof?
- What types of proofs are there?
- How do you know what type of proof to use?
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Staff Review
Have you wondered what it means to "prove" something beyond high school Geometry. Check out this very brief overview of different types of basic proofs. If you're just curious or if you don't understand basic differences between approaches to proofs, this is a great starting point. Now, at least you will understand what your professor means when he or she asks you to prove something. Additional examples or resources could be very helpful, however.
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