A Naturally Occurring Function Continuous only at Irrationals
Amitava Bagchi, Edward M. Reingold · American Mathematical Monthly · 1982
computer science. The function f arises in connection with random binary search trees. We shall only sketch the basic definitions and relevant background material, referring the reader to [2] or [3] for a comprehensive presentation. A binary tree is a finite set of nodes that is either empty or consists of a root and two disjoint binary trees called the left and right subtrees of the root. It is customary to draw such a tree as