## 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 from time to time. Below is the first Q & A in this series.

**Question**

Are all objects with irrational lengths measureable?

**Answer **

Yes. In principle, they are measureable.

The number line represents all real numbers. It contains all the rational and irrational numbers. In fact, there is a one-to-one correspondence between the set of real numbers and the set of points on the number line. This means that every real number has a corresponding point on the number line, and every point on the number line has a corresponding real number. Therefore, since we can locate every irrational number on the number line, we can find its distance from 0. This distance represents the irrational length.