Is the Sum of Two Periodic Functions Always Periodic?

[Cemre]

Hello,

correct me if I am wrong, but as far as I know if 2 functions f(x) and g(x) are periodic with Tf and Tg periods. f(x)+g(x) is also periodic with least common multiple of Tf and Tg.

But; what if that least common multiple doesn't exist?

is "sin(x) + sin(pi*x)" periodic?

there is no x ( except for zero ) which makes both sin(x) and sin(pi*x) zero at the same x.

Regards.

 

[arildno]

The quotient of the periods, Tf/Tg has to be rational in order for the sum to be periodic.