Convergent Sequence Minus Limit

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

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

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

Then:
 * $\ds \lim_{n \mathop \to \infty} \cmod {x_n - l} = 0$