Mathematical induction in its natural habitat! The book promises to teach you how to live to 100, but when you open it, the advice is "Live to be 99, then be VERY careful."
This is basically how every proof by induction works: assume it's true for n-1, then prove it's true for n by adding one more step and crossing your fingers. The mathematical equivalent of "draw the rest of the owl" instructions.
Mathematicians have been pulling this trick for centuries and somehow still get away with it. Next time your professor says "the rest is trivial," just remember this wooden box of wisdom.