July 2011 Week 1 Post Summary
A. Mathematics and Multimedia
Month: July 2011
Geometer’s Sketchpad Essentials Series
Before I became a GeoGebra user, I had been a user of Geometer’s Sketchpad (GSP version 4.07) for quite some time. Although I am a great fan of GeoGebra, GSP requires more mathematical maturity to use, and in several aspects, has also its advantages. Sometimes, I am tempted to write a comparison between the two software, but I fear that I might be biased because I haven’t been using GSP very much nowadays.
This tutorial series will discuss the basics of GSP, and is parallel to the GeoGebra Essentials Series. The future topics are as follows: » Read more
More examples of proof by contradiction
We have had good discussions on mathematical proofs, so I am planning to create a mathematical proof series that will discuss the basics such as direct proof, indirect proof, and proof by mathematical induction. But before I do that, let me continue with more examples of proof by contradiction.
Proof by contradiction, as we have discussed, is a proof strategy where you assume the opposite of a statement, and then find a contradiction somewhere in your proof. Finding a contradiction means that your assumption is false and therefore the statement is true. Below are several more examples of this proof strategy.
Example 1: 
Example 2: 
Example 3: Proof that there are infinitely many primes.
Example 4: Knights and Liars
Example 5: 