Enumerating the Rational Numbers

rational numbers enumerated

1

repeat fractions

reduce fractions

static size

index value: 1 rational: 1/1

This Demonstration shows that the rational numbers are enumerable by visualizing the process of enumerating the fractions in a two-dimensional table. The process illustrates the fact that the Cartesian product of two enumerable sets is enumerable, as the positive rational numbers are a subset of

×

. A nuance here is that many fractions of natural numbers represent the same rational number. With "repeat fractions" unchecked, only distinct rational numbers are enumerated.