Last year, I had a good discussion with some teachers about Venn diagrams. Several teachers commented that I should change the diagram below because it might give an impression that the number of rational numbers is the same as the number of irrational numbers. Sadly, I was not sure if I was able to explain […]

Continue reading…

# Posts tagged with 'irrational numbers'

## Are all objects with irrational lengths measureable?

I was deleting old emails a while ago and I came across with questions from some students reading my blog. I have answered quite a number of questions from middle school and high school students via Email and Facebook since this blog started. I think some are worth publishing here, so I’ll probably post one […]

Continue reading…

## Proof that log 2 is an irrational number

Before doing the proof, let us recall two things: (1) rational numbers are numbers that can be expressed as where and are integers, and not equal to ; and (2) for any positive real number , its logarithm to base is defined to be a number such that . In proving the statement, we use […]

Continue reading…