Proof Techniques - Indirect Proofs

Section 2.2 Materials

Section 2.2 Problem Set

In addition to the ProofSpace screencasts below, we also highly recommend an exploration of the fact that the square root of 2 is irrational. Robert Talbert, of Grand Valley State University, provides an excellent screencast about this fact, which is linked below. We also think it is beneficial to see that there are many different ways to prove this fact, and you can explore several different techniques on the Cut-The-Knot website:
Various proofs that the square root of 2 is irrational.

Section 2.2 Screencasts

Please note that if you are having buffering issues or slow response times for the videos or video controls, this can be alleviated by downloading the video. There is a "Download" button below the viewing screen of each video.

Proof by contradiction: Irrationality of sqrt(2) (Screencast 3.3.4)

(Robert Talbert from the Mathematics Department at Grand Valley State University)

Section 2.2 Supplemental Videos

Here is a selection of supplemental videos related to topics in this section.

• Proof by contraposition (Screencast 3.2.1),
• Proof by Contraposition, part 2 (Screencast 3.2.2),
• Proof by contradiction (Screencast 3.3.1),
• Proof by contradiction, part 2 (Screencast 3.3.2),
• Proof by contradiction, part 3 (Screencast 3.3.3),
• Proof by contradiction: Irrationality of sqrt(2) (Screencast 3.3.4)

These videos were created by Robert Talbert from the Mathematics Department at Grand Valley State University. Click here for more details.