If you get discouraged, keep in mind that the content of this book represents a cleaned-up version of many false starts. For example, John Hubbard started by trying to prove Fubini's theorem in the form presented in Equation 4.5.1. When he failed, he realized (something he had known and forgotten) that the statement was in fact false. He then went through a stack of scrap paper before coming up with a correct proof. Other statements in the book represent the efforts of some of the world's best mathematicians over many years.