Sum of periodic functions

1. What is sum of two periodic functions?
2. Is the sum of two periodic functions still periodic?
3. Can sum of a periodic and non periodic function be periodic?

What is sum of two periodic functions?

The identity function is the sum of two periodic functions

Choose two distinct elements . Then . Let and . Then has period d, has period c, and.

Is the sum of two periodic functions still periodic?

Answer: Not necessarily. It doesn't look periodic because it isn't. The reason is that the two functions have periods that are not rational multiples of each other.

Can sum of a periodic and non periodic function be periodic?

Yes, it is possible. For example, , satisfy the property. is clearly periodic, and the sum, which is is also periodic.