Convergent Sequence Minus Limit/Proof 2

Proof
We note that all of $\Q, \R, \C$ can be considered as metric spaces.

Then under the usual metric:
 * $d \left({x_n, l}\right) = \left|{x_n - l}\right|$.

The result follows from the definition of metric: $d \left({x_n, l}\right) = 0 \iff x_n = l$.