# Enumerating the Rational Numbers

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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.

Contributed by: John Stucky (January 2015)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Reference

[1] E. Maor, *To Infinity and Beyond: A Cultural History of the Infinite*, Princeton, NJ: Princeton University Press, 1991.

## Permanent Citation

"Enumerating the Rational Numbers"

http://demonstrations.wolfram.com/EnumeratingTheRationalNumbers/

Wolfram Demonstrations Project

Published: January 26 2015