Convergent Sequence Minus Limit/Proof 1

Proof
Let $\epsilon > 0$.

We need to show that there exists $N$ such that:
 * $\forall n > N: \size {\paren {\size {x_n - l} - 0} } < \epsilon$

But:
 * $\size {\paren {\size {x_n - l} - 0} } = \size {x_n - l}$

So what needs to be shown is just:
 * $x_n \to l$ as $n \to \infty$

which is the definition of $\displaystyle \lim_{n \mathop \to \infty} x_n = l$.