Chatting with Nat about numerous amusing things in the surrounding world, we came to the following question.

Consider the set of all books written by the mankind. Let's define on this set the following relation: book A relates to book B (denoted as A ~> B) if book B mentioned somewhere in book A.

Well, the notion "mentioned" is somewhat vague, but we can safely assume that to be counted as "mentioned", book B should be unambigously identificable by a non-brain-damaged reader (say, by Nat). Also, there are some complications like Stanislaw Lem's reviews of nonexistent books and books-inside-books a la Borches and Barth, but let's ignore them for the sake of purity.

Consider the transitive closure of the relation "~>" and corresponding equivalent classes on the set of all books. How many equivalent classes there are?