# Enumerating the Rational Numbers

Enumerating the Rational Numbers

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.

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