3-5 switch

Andrew Wiles was having trouble making some connections with his proof, until he figured out this little "trick" the three-five switch. This is covered in chapter 11 of Nigel Boston's book about the proof of Fermat's last theorem. When dealing with an infinite number of possibilities you have to be able to count them. The idea of counting something infinite may sound like it is not possible, but it is as long as what you are using is countable. For example the integers and natural numbers are infinite countable sets, where the reals are an infinite uncountable set. The three-five switch aided in the countability of sets.