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:
 * $\map d {x_n, l} = \cmod {x_n - l}$.

The result follows from the definition of metric:


 * $\map d {x_n, l} = 0 \iff x_n = l$.