QuoteIt is well known (indeed, as Paul Erd½os might have said, every child knows) that the rationals are
countable. However, the standard presentations of this fact do not give an explicit enumeration;
rather they show how to construct an enumeration. In this note we will explicitly describe a
sequence b(n) with the property that every positive rational appears exactly once as b(n)/b(n+1).
Moreover, b(n) is the solution of a quite natural counting problem.
https://www.math.upenn.edu/~wilf/website/recounting.pdf
Infinite Fractions:
https://www.youtube.com/watch?v=DpwUVExX27E