- #1

Dschumanji

- 153

- 1

*Counterexamples: From Elementary Calculus to the Beginning of Calculus*and became interested in the section on periodic functions. I thought of the following question:

Suppose you have a periodic real valued function f(x) with a

__fundamental__period T. Let c be an integer greater than 1. Is it possible for f(x)+f(cx) to have a

__fundamental__period less than T?

Many simple examples would seem to indicate that the answer is no, but I can't find a proof and have failed to develop my own proof. I searched through many other books on counterexamples and can't seem to find an example that would indicate the answer is yes.