Integers can be expressed as rationals, but the number of all rationals is equal to the number of all positive integers. The Stern–Brocot Tree shows this by enumerating the rationals. It was found by the German mathematician Moritz Stern in 1858 and the French clockmaker Achille Brocot in 1860.
R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, 2nd ed., Reading, MA: Addison-Wesley Professional, 1994 pp. 116ff.
Wolfram Demonstrations Project
Published: March 7 2011