Think about how you would specify a book in the "all possible books" library - you would need a number at least as large as the book itself, in the general case

Think about how you would specify a book in the "all possible books" library - you would need a number at least as large as the book itself, in the general case! This might be easier to see if you imagine the "library" as the set of all possible numbers (in binary) up to a certain reasonable maximum. So you specify the book...by giving the binary representation of the book, which is simply its index if you order them by their numerical value. So you can see how having all books in your library is the same as having no books.