Convergent Sequence Minus Limit

Theorem
Let $X$ be one of the standard number fields $\Q, \R, \C$.

Let $\left \langle {x_n} \right \rangle$ be a sequence in $X$ which converges to $l$.

That is:
 * $\displaystyle \lim_{n \mathop \to \infty} x_n = l$

Then:
 * $\displaystyle \lim_{n \mathop \to \infty} \left|{x_n - l}\right| = 0$