If $a_0=o(1)$ ($a_0$ is a constant) is it correct to conclude $ a_0=0$?

Question

About a constant $a_0$ it is given that $a_0=o(1)$ for $x \to 0$. This mean $\lim_{x\to 0}{\frac{a_0}{1}}=0$. But $a_0$ does not depend on $x$, and if the limit for $a_0/1$ is $0$, then $a_0=0$, right?