  Relational Databases are universally conceived as an advance over their
predecessors Network and Hierarchical models. Superior in every querying
respect, they turned out to be surprisingly incomplete when modeling transitive
dependencies. Almost every couple of months a question how to model a tree in
the database surfaces at comp.database.theory newsgroup. This article completes
a series of articles exploring Nested Intervals Model. Previous articles
introduced tree encoding with Binary Rational Numbers. However, binary encoding
grows exponentially, both in breadth and in depth. In this article, we'll
leverage Farey fractions in order to overcome this problem. We'll also
demonstrate that our implementation scales to a tree with 1M nodes.
