I have a little bitty question about a wave function

For a sawtooth wave function with a period of P where the first branch of the function is given for [a, a+P) we can say that :

f(x)=some expression in x for [a, a+P)

f(x+nP)=f(x)

Why is 'a+P' not included in the x-interval? What's gonna happen if we include 'a+P' not included in the x-interval?

Thank You.

I use g(x) for "some expression in x".
and let's include a+P in the x-interval

So you have

f(x) = g(x) when x is in [a, a+p]

When you plug x =a+p, you get

f(a+p) = g(a+p)...(1)

On the other hand, f(x+nP) = g(x) and if you plug n=1and x=a, you get

f(a+p) = g(a) ...(2)

Comparing (1) and (2), you get g(a) = g(a+p); but g(a+p) does not necessarily equal g(a).

And that's why a+P is not included in the interval

f(x) =0 for x =a and f(x) =0 for x =a+P these boundary conditions are needed, otherwise the function will never represent want is demanded, this wave function crosses the x-axis at x=a, goes all the way up or down closing half the wave length (or the total wavelength of the first branch) at x= a+P.
need to see some more