Let $\lim _{n \rightarrow \infty} x_{n}=x$. Then which of the following is $\text{TRUE.}$
- There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right|=0$.
- There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right| \leq \epsilon$ for any $\epsilon>0$.
- For every $\epsilon>0$, there exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right| \leq \epsilon$.
- There exists an $n_{0}$, such that for all $n>n_{0},\left|\frac{x_{n}}{x}\right| \leq \epsilon$ for any $\epsilon>0$.
- None of the above.