Ok as we know, if $f(x+P) = f(x)$ then the function is periodic.

So if the function is not periodic, $f(x+p) = f(x)$, what it the value of p?

It's just a positive real number, for example the $f(x)=\sin(x)$ is periodic with periodicity $2\pi$ which is a positive real number.

But in that: case f(x)is periodic.

for a function not periodic , the period is a positive real number too?

Originally Posted by Fabio010
Ok as we know, if $f(x+P) = f(x)$ then the function is periodic.

So if the function is not periodic, $f(x+p) = f(x)$, what it the value of p?
If this always true $f(x+0)=f(x)~?$

So you are telling me that in not periodic functions P = 0?

If you know that $f(x)$ is not periodic but for all $x$ you have $f(x+P)=f(x)$ then $P=~?$