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Enumerating the Rational Numbers

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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.
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