If fff has period TTT, prove f(x+nT)=f(x)f(x + nT) = f(x)f(x+nT)=f(x) for integer nnn.
By induction using f(x+T)=f(x)f(x+T) = f(x)f(x+T)=f(x)
Not true for n<0n < 0n<0
Only for n>0n > 0n>0
Requires continuity