The ancient Greeks wondered when irrational numbers, like pi, can be represented with fractions. Two mathematicians now have a complete answer.

Rational numbers can be expressed as the ratio of two integers, while irrational numbers, such as square roots of non-square numbers, cannot.

We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many ...