# Chapter 3 Integer Functions

## 3.3 Floor/Ceiling Recurrences

“In trying to devise a proof by mathematical induction, you may fail for two opposite reasons. You may fail because you try to prove too much: Your $P(n)$ is too heavy a burden. Yet you may also fail because you try to prove too little: Your $P(n)$ is too weak a support. In general, you have to balance the statement of your theorem so that the support is just enough for the burden.”

— George Pólya, Induction and Analogy in Mathematics