Let $$f : \mathbb{R} \to \mathbb{R}$$ be a function defined by

$$f(x) = \begin{cases} x^2 \sin\left(\frac{\pi}{x^2}\right), & \text{if } x \neq 0, \\ 0, & \text{if } x = 0. \end{cases}$$

Then which of the following statements is TRUE?

A

$$f(x) = 0$$ has infinitely many solutions in the interval $$\left[\frac{1}{10^{10}}, \infty\right)$$.

B

$$f(x) = 0$$ has no solutions in the interval $$\left[\frac{1}{\pi}, \infty\right)$$.

C

The set of solutions of $$f(x) = 0$$ in the interval $$\left(0, \frac{1}{10^{10}}\right)$$ is finite.

D

$$f(x) = 0$$ has more than 25 solutions in the interval $$\left(\frac{1}{\pi^2}, \frac{1}{\pi}\right)$$.