ABSTRACT
This proof technique is more complicated than the previous techniques, so it merits a chapter of its own. But there’s only so much to say about mathematical induction, and then you just have to practice this proof technique for yourself. The basic idea is to reduce a theorem to a smaller case of the same theorem, and then to a smaller case, and so on to a small case you can deal with manually. Example 4.2.5 is particularly important, first because it shows why one must reduce to a previously known case (rather than building up from a known case), and second because it is a result we will use regularly in Chapters 10-13.
