7. For any $x \in \mathbf{R}, f(x)=|\sin x|$. When $n \leqslant x<n+1$ ( $n$ is an integer), $g(x)=x-n$, then among $f(x), g(x), f(x)+g(x), f(x) g(x)$, the number of periodic functions is $\qquad$
7. Let $f(x), g(x)$ both be periodic functions with the smallest positive periods being $\pi, 1$ respectively. $f(x)+g(x)$ and $f(x) g(x)$ are not periodic functions. In fact, if $f(x)+g(x)$ is a periodic function, and $T$ is one of its periods, then for any $x \in \mathbf{R}$, we have
$$
f(x+T)+g(x+T)=f(x)+g(x) .
$$

In (1), let $x=0$, then $f(T)+g(T)=f(0)+g(0)=0$. Since $f(T) \geqslant 0, g(T) \geqslant 0$, it follows that $f(T)=0, g(T)=0$. From $f(T)=0$, we get $T=k \pi$ (where $k$ is an integer), and from $g(T)=0$, we get $T=m$ (where $k, m$ are integers), so $m=k \pi$, which is a contradiction. Similarly, it can be shown that $f(x) g(x)$ is not a periodic function.