By Florian Cajori
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Additional info for A History of Mathematical Notations Volume II, Notations Mainly in Higher Mathematics
11] G. H. Hardy and E. M. Wright, The Theory of Numbers, Oxford University Press, 1956.  Donald E. Knuth, The Art of Computer Programming, Vol. 3, Addison-Wesley, Reading, 1973.  Albert Nijenhuis and Herbert S. , Academic Press, New York, 1978.  Kathleen M. O’Hara, Bijections for partition identities. J. Combin. Theory Ser. A 49 (1988), no. 1, 13–25.  Hans Rademacher, On the partition function p(n), Proc. London Math. Soc. 43 (1937), 241–254. 35  Jeffrey B. Remmel, Bijective proofs of some classical partition identities, J.
That is, b(n) and b(n + 1) are relatively prime, and each positive reduced rational number occurs once and only once in the list b(0)/b(1), b(1)/b(2), . .. D. dissertation), June 1987.  George E. Andrews, The Theory of Partitions, Encycl. Math. Appl. 2, AddisonWesley, Reading, MA 1976.  Neil Calkin and Herbert S. Wilf, Recounting the Rationals, Amer. Math. Monthly 107 (2000), 360–363.  Sylvie Corteel, Carla D. Savage, Herbert S. Wilf and Doron Zeilberger, A pentagonal number sieve, J.
J We show the following properties of this tree. 1. The numerator and denominator at each vertex are relatively prime. This is certainly true at the top vertex. Otherwise, suppose r/s is a vertex on the highest possible level of the tree for which this is false. If r/s is a left child, then its parent is r/(s − r), which would clearly also not be a reduced fraction, and would be on a higher level, a contradiction. If r/s is a right child, then its parent is (r − s)/s, which leads to the same contradiction.
A History of Mathematical Notations Volume II, Notations Mainly in Higher Mathematics by Florian Cajori